Solve Using the Quadratic Formula 8x^2+5x=3+7x

$8 x^{2} + 5 x = 3 + 7 x$

Step 1

Move all terms to the left side of the equation and simplify.

Move all the expressions to the left side of the equation.

Subtract $3$ from both sides of the equation.

$8 x^{2} + 5 x - 3 = 7 x$

Subtract $7 x$ from both sides of the equation.

$8 x^{2} + 5 x - 3 - 7 x = 0$

Subtract $7 x$ from $5 x$ .

$8 x^{2} - 2 x - 3 = 0$

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = 8$ , $b = - 2$ , and $c = - 3$ into the quadratic formula and solve for $x$ .

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

Step 4

Simplify.

Simplify the numerator.

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

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

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

Multiply $- 4$ by $8$ .

$x = \frac{2 \pm \sqrt{4 - 32 \cdot - 3}}{2 \cdot 8}$

Multiply $- 32$ by $- 3$ .

$x = \frac{2 \pm \sqrt{4 + 96}}{2 \cdot 8}$

Add $4$ and $96$ .

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

Rewrite $100$ as $10^{2}$ .

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

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

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

Multiply $2$ by $8$ .

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

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

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

Step 5

The final answer is the combination of both solutions.

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