6x(2x+50)=180

Solution for 6x(2x+50)=180 equation:

6x(2x+50)=180

We move all terms to the left:

6x(2x+50)-(180)=0

We multiply parentheses

12x^2+300x-180=0

a = 12; b = 300; c = -180;
Δ = b2-4ac
Δ = 3002-4·12·(-180)
Δ = 98640
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:

$\sqrt{\Delta}=\sqrt{98640}=\sqrt{144*685}=\sqrt{144}*\sqrt{685}=12\sqrt{685}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-12\sqrt{685}}{2*12}=\frac{-300-12\sqrt{685}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+12\sqrt{685}}{2*12}=\frac{-300+12\sqrt{685}}{24}
$