3x(4x+5)=180

Solution for 3x(4x+5)=180 equation:

3x(4x+5)=180

We move all terms to the left:

3x(4x+5)-(180)=0

We multiply parentheses

12x^2+15x-180=0

a = 12; b = 15; c = -180;
Δ = b2-4ac
Δ = 152-4·12·(-180)
Δ = 8865
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:

$\sqrt{\Delta}=\sqrt{8865}=\sqrt{9*985}=\sqrt{9}*\sqrt{985}=3\sqrt{985}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{985}}{2*12}=\frac{-15-3\sqrt{985}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{985}}{2*12}=\frac{-15+3\sqrt{985}}{24}
$