3x^2-4x=72

Solution for 3x^2-4x=72 equation:

3x^2-4x=72

We move all terms to the left:

3x^2-4x-(72)=0

a = 3; b = -4; c = -72;
Δ = b2-4ac
Δ = -42-4·3·(-72)
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{55}}{2*3}=\frac{4-4\sqrt{55}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{55}}{2*3}=\frac{4+4\sqrt{55}}{6}
$