(w-11)(3w-11)=137

Solution for (w-11)(3w-11)=137 equation:

(w-11)(3w-11)=137

We move all terms to the left:

(w-11)(3w-11)-(137)=0

We multiply parentheses ..

(+3w^2-11w-33w+121)-137=0

We get rid of parentheses

3w^2-11w-33w+121-137=0

We add all the numbers together, and all the variables

3w^2-44w-16=0

a = 3; b = -44; c = -16;
Δ = b2-4ac
Δ = -442-4·3·(-16)
Δ = 2128
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:

$\sqrt{\Delta}=\sqrt{2128}=\sqrt{16*133}=\sqrt{16}*\sqrt{133}=4\sqrt{133}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{133}}{2*3}=\frac{44-4\sqrt{133}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{133}}{2*3}=\frac{44+4\sqrt{133}}{6}
$