(u+1)(u-5)=27

Solution for (u+1)(u-5)=27 equation:

(u+1)(u-5)=27

We move all terms to the left:

(u+1)(u-5)-(27)=0

We multiply parentheses ..

(+u^2-5u+u-5)-27=0

We get rid of parentheses

u^2-5u+u-5-27=0

We add all the numbers together, and all the variables

u^2-4u-32=0

a = 1; b = -4; c = -32;
Δ = b2-4ac
Δ = -42-4·1·(-32)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-12}{2*1}=\frac{-8}{2}
=-4
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+12}{2*1}=\frac{16}{2}
=8
$