32x^2+24x=72

Solution for 32x^2+24x=72 equation:

32x^2+24x=72

We move all terms to the left:

32x^2+24x-(72)=0

a = 32; b = 24; c = -72;
Δ = b2-4ac
Δ = 242-4·32·(-72)
Δ = 9792
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:

$\sqrt{\Delta}=\sqrt{9792}=\sqrt{576*17}=\sqrt{576}*\sqrt{17}=24\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24\sqrt{17}}{2*32}=\frac{-24-24\sqrt{17}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24\sqrt{17}}{2*32}=\frac{-24+24\sqrt{17}}{64}
$