4w^2-12w=20

Solution for 4w^2-12w=20 equation:

4w^2-12w=20

We move all terms to the left:

4w^2-12w-(20)=0

a = 4; b = -12; c = -20;
Δ = b2-4ac
Δ = -122-4·4·(-20)
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{29}}{2*4}=\frac{12-4\sqrt{29}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{29}}{2*4}=\frac{12+4\sqrt{29}}{8}
$