Solve for x -7x+8-10x^2=7

$- 7 x + 8 - 10 x^{2} = 7$

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

Subtract $7$ from both sides of the equation.

$- 7 x + 8 - 10 x^{2} - 7 = 0$

Subtract $7$ from $8$ .

$- 7 x - 10 x^{2} + 1 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = - 10$ , $b = - 7$ , and $c = 1$ into the quadratic formula and solve for $x$ .

$\frac{7 \pm \sqrt{{(- 7)}^{2} - 4 \cdot (- 10 \cdot 1)}}{2 \cdot - 10}$

Simplify.

Simplify the numerator.

Raise $- 7$ to the power of $2$ .

$x = \frac{7 \pm \sqrt{49 - 4 \cdot - 10 \cdot 1}}{2 \cdot - 10}$

Multiply $- 4$ by $- 10$ .

$x = \frac{7 \pm \sqrt{49 + 40 \cdot 1}}{2 \cdot - 10}$

Multiply $40$ by $1$ .

$x = \frac{7 \pm \sqrt{49 + 40}}{2 \cdot - 10}$

Add $49$ and $40$ .

$x = \frac{7 \pm \sqrt{89}}{2 \cdot - 10}$

Multiply $2$ by $- 10$ .

$x = \frac{7 \pm \sqrt{89}}{- 20}$

Move the negative in front of the fraction.

$x = - \frac{7 \pm \sqrt{89}}{20}$

The final answer is the combination of both solutions.

$x = - \frac{7 + \sqrt{89}}{20}, - \frac{7 - \sqrt{89}}{20}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{7 + \sqrt{89}}{20}, - \frac{7 - \sqrt{89}}{20}$

Decimal Form:

$x = - 0.82169905 \dots, 0.12169905 \dots$