Solve Using the Quadratic Formula 8x^2+10x+3=0

$8 x^{2} + 10 x + 3 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 8$ , $b = 10$ , and $c = 3$ into the quadratic formula and solve for $x$ .

$\frac{- 10 \pm \sqrt{10^{2} - 4 \cdot (8 \cdot 3)}}{2 \cdot 8}$

Step 3

Simplify.

Simplify the numerator.

Raise $10$ to the power of $2$ .

$x = \frac{- 10 \pm \sqrt{100 - 4 \cdot 8 \cdot 3}}{2 \cdot 8}$

Multiply $- 4 \cdot 8 \cdot 3$ .

Multiply $- 4$ by $8$ .

$x = \frac{- 10 \pm \sqrt{100 - 32 \cdot 3}}{2 \cdot 8}$

Multiply $- 32$ by $3$ .

$x = \frac{- 10 \pm \sqrt{100 - 96}}{2 \cdot 8}$

Subtract $96$ from $100$ .

$x = \frac{- 10 \pm \sqrt{4}}{2 \cdot 8}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 10 \pm \sqrt{2^{2}}}{2 \cdot 8}$

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

$x = \frac{- 10 \pm 2}{2 \cdot 8}$

Multiply $2$ by $8$ .

$x = \frac{- 10 \pm 2}{16}$

Simplify $\frac{- 10 \pm 2}{16}$ .

$x = \frac{- 5 \pm 1}{8}$

Step 4

The final answer is the combination of both solutions.

$x = - \frac{1}{2}, - \frac{3}{4}$