(2x-15)11x=180

Solution for (2x-15)11x=180 equation:

(2x-15)11x=180

We move all terms to the left:

(2x-15)11x-(180)=0

We multiply parentheses

22x^2-165x-180=0

a = 22; b = -165; c = -180;
Δ = b2-4ac
Δ = -1652-4·22·(-180)
Δ = 43065
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{43065}=\sqrt{9*4785}=\sqrt{9}*\sqrt{4785}=3\sqrt{4785}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-165)-3\sqrt{4785}}{2*22}=\frac{165-3\sqrt{4785}}{44}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-165)+3\sqrt{4785}}{2*22}=\frac{165+3\sqrt{4785}}{44}
$