(w-4)(w-11)=-12

Solution for (w-4)(w-11)=-12 equation:

(w-4)(w-11)=-12

We move all terms to the left:

(w-4)(w-11)-(-12)=0

We add all the numbers together, and all the variables

(w-4)(w-11)+12=0

We multiply parentheses ..

(+w^2-11w-4w+44)+12=0

We get rid of parentheses

w^2-11w-4w+44+12=0

We add all the numbers together, and all the variables

w^2-15w+56=0

a = 1; b = -15; c = +56;
Δ = b2-4ac
Δ = -152-4·1·56
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-1}{2*1}=\frac{14}{2}
=7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+1}{2*1}=\frac{16}{2}
=8
$