5x(3x+12)=72

Solution for 5x(3x+12)=72 equation:

5x(3x+12)=72

We move all terms to the left:

5x(3x+12)-(72)=0

We multiply parentheses

15x^2+60x-72=0

a = 15; b = 60; c = -72;
Δ = b2-4ac
Δ = 602-4·15·(-72)
Δ = 7920
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:

$\sqrt{\Delta}=\sqrt{7920}=\sqrt{144*55}=\sqrt{144}*\sqrt{55}=12\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-12\sqrt{55}}{2*15}=\frac{-60-12\sqrt{55}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+12\sqrt{55}}{2*15}=\frac{-60+12\sqrt{55}}{30}
$