Solve Using the Quadratic Formula 3x^2-2x-5=0

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Algebra

$3 x^{2} - 2 x - 5 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 3$ , $b = - 2$ , and $c = - 5$ into the quadratic formula and solve for $x$ .

$\frac{2 \pm \sqrt{{(- 2)}^{2} - 4 \cdot (3 \cdot - 5)}}{2 \cdot 3}$

Simplify.

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Simplify the numerator.

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Raise $- 2$ to the power of $2$ .

$x = \frac{2 \pm \sqrt{4 - 4 \cdot 3 \cdot - 5}}{2 \cdot 3}$

Multiply $- 4$ by $3$ .

$x = \frac{2 \pm \sqrt{4 - 12 \cdot - 5}}{2 \cdot 3}$

Multiply $- 12$ by $- 5$ .

$x = \frac{2 \pm \sqrt{4 + 60}}{2 \cdot 3}$

Add $4$ and $60$ .

$x = \frac{2 \pm \sqrt{64}}{2 \cdot 3}$

Rewrite $64$ as $8^{2}$ .

$x = \frac{2 \pm \sqrt{8^{2}}}{2 \cdot 3}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{2 \pm 8}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{2 \pm 8}{6}$

Simplify $\frac{2 \pm 8}{6}$ .

$x = \frac{1 \pm 4}{3}$

The final answer is the combination of both solutions.

$x = \frac{5}{3}, - 1$

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Name

Name	one billion four hundred forty-five million five hundred seventy-seven thousand two hundred seventy

Interesting facts

1445577270 has 16 divisors, whose sum is 3469385520
The reverse of 1445577270 is 0727755441
Previous prime number is 3

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 42
Digital Root 6

Name

Name	four hundred fifty-two million thirty-four thousand nineteen

Interesting facts

452034019 has 16 divisors, whose sum is 482049792
The reverse of 452034019 is 910430254
Previous prime number is 83

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 28
Digital Root 1

Name

Name	four hundred fifty-four million nine hundred sixty thousand five hundred forty-five

Interesting facts

454960545 has 64 divisors, whose sum is 842171904
The reverse of 454960545 is 545069454
Previous prime number is 71

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 42
Digital Root 6

Graph f(x)=x^2-8x+15

Simplify (3x-2)(3x+2)

Simplify (3-2i)(3+2i)

Simplify (x^5)^3

Factor by Grouping 3x^2+6x-x-2