(4w-6)(2w)=180

Solution for (4w-6)(2w)=180 equation:

(4w-6)(2w)=180

We move all terms to the left:

(4w-6)(2w)-(180)=0

We multiply parentheses

8w^2-12w-180=0

a = 8; b = -12; c = -180;
Δ = b2-4ac
Δ = -122-4·8·(-180)
Δ = 5904
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:

$\sqrt{\Delta}=\sqrt{5904}=\sqrt{144*41}=\sqrt{144}*\sqrt{41}=12\sqrt{41}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{41}}{2*8}=\frac{12-12\sqrt{41}}{16}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{41}}{2*8}=\frac{12+12\sqrt{41}}{16}
$