5x(x+40)=180

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

5x(x+40)=180

We move all terms to the left:

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

We multiply parentheses

5x^2+200x-180=0

a = 5; b = 200; c = -180;
Δ = b2-4ac
Δ = 2002-4·5·(-180)
Δ = 43600
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:

$\sqrt{\Delta}=\sqrt{43600}=\sqrt{400*109}=\sqrt{400}*\sqrt{109}=20\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-20\sqrt{109}}{2*5}=\frac{-200-20\sqrt{109}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+20\sqrt{109}}{2*5}=\frac{-200+20\sqrt{109}}{10}
$