(11w)(5w+4)=360

Solution for (11w)(5w+4)=360 equation:

(11w)(5w+4)=360

We move all terms to the left:

(11w)(5w+4)-(360)=0

We multiply parentheses

55w^2+44w-360=0

a = 55; b = 44; c = -360;
Δ = b2-4ac
Δ = 442-4·55·(-360)
Δ = 81136
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:

$\sqrt{\Delta}=\sqrt{81136}=\sqrt{16*5071}=\sqrt{16}*\sqrt{5071}=4\sqrt{5071}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{5071}}{2*55}=\frac{-44-4\sqrt{5071}}{110}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{5071}}{2*55}=\frac{-44+4\sqrt{5071}}{110}
$