w^2-54=15w

Solution for w^2-54=15w equation:

w^2-54=15w

We move all terms to the left:

w^2-54-(15w)=0

a = 1; b = -15; c = -54;
Δ = b2-4ac
Δ = -152-4·1·(-54)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-21}{2*1}=\frac{-6}{2}
=-3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+21}{2*1}=\frac{36}{2}
=18
$