5x(6x-11)=180

Solution for 5x(6x-11)=180 equation:

5x(6x-11)=180

We move all terms to the left:

5x(6x-11)-(180)=0

We multiply parentheses

30x^2-55x-180=0

a = 30; b = -55; c = -180;
Δ = b2-4ac
Δ = -552-4·30·(-180)
Δ = 24625
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:

$\sqrt{\Delta}=\sqrt{24625}=\sqrt{25*985}=\sqrt{25}*\sqrt{985}=5\sqrt{985}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-5\sqrt{985}}{2*30}=\frac{55-5\sqrt{985}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+5\sqrt{985}}{2*30}=\frac{55+5\sqrt{985}}{60}
$