5x(8x+11)=180

Solution for 5x(8x+11)=180 equation:

5x(8x+11)=180

We move all terms to the left:

5x(8x+11)-(180)=0

We multiply parentheses

40x^2+55x-180=0

a = 40; b = 55; c = -180;
Δ = b2-4ac
Δ = 552-4·40·(-180)
Δ = 31825
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:

$\sqrt{\Delta}=\sqrt{31825}=\sqrt{25*1273}=\sqrt{25}*\sqrt{1273}=5\sqrt{1273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-5\sqrt{1273}}{2*40}=\frac{-55-5\sqrt{1273}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+5\sqrt{1273}}{2*40}=\frac{-55+5\sqrt{1273}}{80}
$