4x^2+24x=60

Solution for 4x^2+24x=60 equation:

4x^2+24x=60

We move all terms to the left:

4x^2+24x-(60)=0

a = 4; b = 24; c = -60;
Δ = b2-4ac
Δ = 242-4·4·(-60)
Δ = 1536
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:

$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-16\sqrt{6}}{2*4}=\frac{-24-16\sqrt{6}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+16\sqrt{6}}{2*4}=\frac{-24+16\sqrt{6}}{8}
$