# Which are the solutions of the quadratic equation x^2=7x+4?

Jul 8, 2018

$x = \frac{7}{2} \pm \frac{\sqrt{65}}{2}$

#### Explanation:

Given: ${x}^{2} = 7 x + 4$

Put the equation in $A {x}^{2} + B x + C = 0$ form.

${x}^{2} - 7 x - 4 = 0$

Use the quadratic formula to solve:

$x = \frac{- B \pm \sqrt{{B}^{2} - 4 A C}}{2 A}$

$x = \frac{7 \pm \sqrt{49 - 4 \left(1\right) \left(- 4\right)}}{2}$

$x = \frac{7}{2} \pm \frac{\sqrt{65}}{2}$