2w^2-12w=54

Solution for 2w^2-12w=54 equation:

2w^2-12w=54

We move all terms to the left:

2w^2-12w-(54)=0

a = 2; b = -12; c = -54;
Δ = b2-4ac
Δ = -122-4·2·(-54)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-24}{2*2}=\frac{-12}{4}
=-3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+24}{2*2}=\frac{36}{4}
=9
$