4w^2-12w=24

Solution for 4w^2-12w=24 equation:

4w^2-12w=24

We move all terms to the left:

4w^2-12w-(24)=0

a = 4; b = -12; c = -24;
Δ = b2-4ac
Δ = -122-4·4·(-24)
Δ = 528
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{33}}{2*4}=\frac{12-4\sqrt{33}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{33}}{2*4}=\frac{12+4\sqrt{33}}{8}
$