11w(5w+4)=180

Solution for 11w(5w+4)=180 equation:

11w(5w+4)=180

We move all terms to the left:

11w(5w+4)-(180)=0

We multiply parentheses

55w^2+44w-180=0

a = 55; b = 44; c = -180;
Δ = b2-4ac
Δ = 442-4·55·(-180)
Δ = 41536
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:

$\sqrt{\Delta}=\sqrt{41536}=\sqrt{64*649}=\sqrt{64}*\sqrt{649}=8\sqrt{649}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-8\sqrt{649}}{2*55}=\frac{-44-8\sqrt{649}}{110}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+8\sqrt{649}}{2*55}=\frac{-44+8\sqrt{649}}{110}
$