(u+7)(u+5)=8

Solution for (u+7)(u+5)=8 equation:

(u+7)(u+5)=8

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

u^2+5u+7u+35-8=0

We add all the numbers together, and all the variables

u^2+12u+27=0

a = 1; b = 12; c = +27;
Δ = b2-4ac
Δ = 122-4·1·27
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6}{2*1}=\frac{-18}{2}
=-9
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6}{2*1}=\frac{-6}{2}
=-3
$