Solve for x x^2+bx+c=0

$x^{2} + b x + c = 0$

Use the quadratic formula to find the solutions.

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

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

$\frac{- b \pm \sqrt{b^{2} - 4 \cdot (1 \cdot c)}}{2 \cdot 1}$

Simplify.

Multiply $- 4$ by $1$ .

$x = \frac{- b \pm \sqrt{b^{2} - 4 c}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- b \pm \sqrt{b^{2} - 4 c}}{2}$

The final answer is the combination of both solutions.

$x = - \frac{b - \sqrt{b^{2} - 4 c}}{2}$

$x = - \frac{b + \sqrt{b^{2} - 4 c}}{2}$