(3x)(8x+15)=180

Solution for (3x)(8x+15)=180 equation:

(3x)(8x+15)=180

We move all terms to the left:

(3x)(8x+15)-(180)=0

We multiply parentheses

24x^2+45x-180=0

a = 24; b = 45; c = -180;
Δ = b2-4ac
Δ = 452-4·24·(-180)
Δ = 19305
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:

$\sqrt{\Delta}=\sqrt{19305}=\sqrt{9*2145}=\sqrt{9}*\sqrt{2145}=3\sqrt{2145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{2145}}{2*24}=\frac{-45-3\sqrt{2145}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{2145}}{2*24}=\frac{-45+3\sqrt{2145}}{48}
$