4w^2+8w=24

Solution for 4w^2+8w=24 equation:

4w^2+8w=24

We move all terms to the left:

4w^2+8w-(24)=0

a = 4; b = 8; c = -24;
Δ = b2-4ac
Δ = 82-4·4·(-24)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{7}}{2*4}=\frac{-8-8\sqrt{7}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{7}}{2*4}=\frac{-8+8\sqrt{7}}{8}
$