10x(6x+20)=180

Solution for 10x(6x+20)=180 equation:

10x(6x+20)=180

We move all terms to the left:

10x(6x+20)-(180)=0

We multiply parentheses

60x^2+200x-180=0

a = 60; b = 200; c = -180;
Δ = b2-4ac
Δ = 2002-4·60·(-180)
Δ = 83200
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:

$\sqrt{\Delta}=\sqrt{83200}=\sqrt{6400*13}=\sqrt{6400}*\sqrt{13}=80\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-80\sqrt{13}}{2*60}=\frac{-200-80\sqrt{13}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+80\sqrt{13}}{2*60}=\frac{-200+80\sqrt{13}}{120}
$