(w-5)*w=126

Solution for (w-5)*w=126 equation:

(w-5)*w=126

We move all terms to the left:

(w-5)*w-(126)=0

We multiply parentheses

w^2-5w-126=0

a = 1; b = -5; c = -126;
Δ = b2-4ac
Δ = -52-4·1·(-126)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-23}{2*1}=\frac{-18}{2}
=-9
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+23}{2*1}=\frac{28}{2}
=14
$