5x(9x+40)=120

Solution for 5x(9x+40)=120 equation:

5x(9x+40)=120

We move all terms to the left:

5x(9x+40)-(120)=0

We multiply parentheses

45x^2+200x-120=0

a = 45; b = 200; c = -120;
Δ = b2-4ac
Δ = 2002-4·45·(-120)
Δ = 61600
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:

$\sqrt{\Delta}=\sqrt{61600}=\sqrt{400*154}=\sqrt{400}*\sqrt{154}=20\sqrt{154}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-20\sqrt{154}}{2*45}=\frac{-200-20\sqrt{154}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+20\sqrt{154}}{2*45}=\frac{-200+20\sqrt{154}}{90}
$