(u+5)(u+3)=8

Solution for (u+5)(u+3)=8 equation:

(u+5)(u+3)=8

We move all terms to the left:

(u+5)(u+3)-(8)=0

We multiply parentheses ..

(+u^2+3u+5u+15)-8=0

We get rid of parentheses

u^2+3u+5u+15-8=0

We add all the numbers together, and all the variables

u^2+8u+7=0

a = 1; b = 8; c = +7;
Δ = b2-4ac
Δ = 82-4·1·7
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{-(8)-6}{2*1}=\frac{-14}{2}
=-7
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6}{2*1}=\frac{-2}{2}
=-1
$