1.1x(x-135)=180

Solution for 1.1x(x-135)=180 equation:

1.1x(x-135)=180

We move all terms to the left:

1.1x(x-135)-(180)=0

We multiply parentheses

x^2-135x-180=0

a = 1; b = -135; c = -180;
Δ = b2-4ac
Δ = -1352-4·1·(-180)
Δ = 18945
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:

$\sqrt{\Delta}=\sqrt{18945}=\sqrt{9*2105}=\sqrt{9}*\sqrt{2105}=3\sqrt{2105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-135)-3\sqrt{2105}}{2*1}=\frac{135-3\sqrt{2105}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+3\sqrt{2105}}{2*1}=\frac{135+3\sqrt{2105}}{2}
$