3x(2x-25)=180

Solution for 3x(2x-25)=180 equation:

3x(2x-25)=180

We move all terms to the left:

3x(2x-25)-(180)=0

We multiply parentheses

6x^2-75x-180=0

a = 6; b = -75; c = -180;
Δ = b2-4ac
Δ = -752-4·6·(-180)
Δ = 9945
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:

$\sqrt{\Delta}=\sqrt{9945}=\sqrt{9*1105}=\sqrt{9}*\sqrt{1105}=3\sqrt{1105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-3\sqrt{1105}}{2*6}=\frac{75-3\sqrt{1105}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+3\sqrt{1105}}{2*6}=\frac{75+3\sqrt{1105}}{12}
$