(u+7)(u+3)=12

Solution for (u+7)(u+3)=12 equation:

(u+7)(u+3)=12

We move all terms to the left:

(u+7)(u+3)-(12)=0

We multiply parentheses ..

(+u^2+3u+7u+21)-12=0

We get rid of parentheses

u^2+3u+7u+21-12=0

We add all the numbers together, and all the variables

u^2+10u+9=0

a = 1; b = 10; c = +9;
Δ = b2-4ac
Δ = 102-4·1·9
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-8}{2*1}=\frac{-18}{2}
=-9
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+8}{2*1}=\frac{-2}{2}
=-1
$