5x(9x+40)=180

Solution for 5x(9x+40)=180 equation:

5x(9x+40)=180

We move all terms to the left:

5x(9x+40)-(180)=0

We multiply parentheses

45x^2+200x-180=0

a = 45; b = 200; c = -180;
Δ = b2-4ac
Δ = 2002-4·45·(-180)
Δ = 72400
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:

$\sqrt{\Delta}=\sqrt{72400}=\sqrt{400*181}=\sqrt{400}*\sqrt{181}=20\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-20\sqrt{181}}{2*45}=\frac{-200-20\sqrt{181}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+20\sqrt{181}}{2*45}=\frac{-200+20\sqrt{181}}{90}
$