7=x^2+8x

Solution for 7=x^2+8x equation:

7=x^2+8x

We move all terms to the left:

7-(x^2+8x)=0

We get rid of parentheses

-x^2-8x+7=0

We add all the numbers together, and all the variables

-1x^2-8x+7=0

a = -1; b = -8; c = +7;
Δ = b2-4ac
Δ = -82-4·(-1)·7
Δ = 92
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{23}}{2*-1}=\frac{8-2\sqrt{23}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{23}}{2*-1}=\frac{8+2\sqrt{23}}{-2}
$