72x^2+3x=288

Solution for 72x^2+3x=288 equation:

72x^2+3x=288

We move all terms to the left:

72x^2+3x-(288)=0

a = 72; b = 3; c = -288;
Δ = b2-4ac
Δ = 32-4·72·(-288)
Δ = 82953
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:

$\sqrt{\Delta}=\sqrt{82953}=\sqrt{9*9217}=\sqrt{9}*\sqrt{9217}=3\sqrt{9217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{9217}}{2*72}=\frac{-3-3\sqrt{9217}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{9217}}{2*72}=\frac{-3+3\sqrt{9217}}{144}
$