75=x^2+8x

Solution for 75=x^2+8x equation:

75=x^2+8x

We move all terms to the left:

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

We get rid of parentheses

-x^2-8x+75=0

We add all the numbers together, and all the variables

-1x^2-8x+75=0

a = -1; b = -8; c = +75;
Δ = b2-4ac
Δ = -82-4·(-1)·75
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{91}}{2*-1}=\frac{8-2\sqrt{91}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{91}}{2*-1}=\frac{8+2\sqrt{91}}{-2}
$