2x(3x+50)=180

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

2x(3x+50)=180

We move all terms to the left:

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

We multiply parentheses

6x^2+100x-180=0

a = 6; b = 100; c = -180;
Δ = b2-4ac
Δ = 1002-4·6·(-180)
Δ = 14320
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:

$\sqrt{\Delta}=\sqrt{14320}=\sqrt{16*895}=\sqrt{16}*\sqrt{895}=4\sqrt{895}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-4\sqrt{895}}{2*6}=\frac{-100-4\sqrt{895}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+4\sqrt{895}}{2*6}=\frac{-100+4\sqrt{895}}{12}
$