50(3x-10)(2x)=180

Solution for 50(3x-10)(2x)=180 equation:

50(3x-10)(2x)=180

We move all terms to the left:

50(3x-10)(2x)-(180)=0

We multiply parentheses

300x^2-1000x-180=0

a = 300; b = -1000; c = -180;
Δ = b2-4ac
Δ = -10002-4·300·(-180)
Δ = 1216000
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:

$\sqrt{\Delta}=\sqrt{1216000}=\sqrt{6400*190}=\sqrt{6400}*\sqrt{190}=80\sqrt{190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-80\sqrt{190}}{2*300}=\frac{1000-80\sqrt{190}}{600}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+80\sqrt{190}}{2*300}=\frac{1000+80\sqrt{190}}{600}
$