(X+7)(5-x)=8

Solution for (X+7)(5-x)=8 equation:

(X+7)(5-X)=8

We move all terms to the left:

(X+7)(5-X)-(8)=0

We add all the numbers together, and all the variables

(X+7)(-1X+5)-8=0

We multiply parentheses ..

(-1X^2+5X-7X+35)-8=0

We get rid of parentheses

-1X^2+5X-7X+35-8=0

We add all the numbers together, and all the variables

-1X^2-2X+27=0

a = -1; b = -2; c = +27;
Δ = b2-4ac
Δ = -22-4·(-1)·27
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{7}}{2*-1}=\frac{2-4\sqrt{7}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{7}}{2*-1}=\frac{2+4\sqrt{7}}{-2}
$