3x^2-4x=172

Solution for 3x^2-4x=172 equation:

3x^2-4x=172

We move all terms to the left:

3x^2-4x-(172)=0

a = 3; b = -4; c = -172;
Δ = b2-4ac
Δ = -42-4·3·(-172)
Δ = 2080
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:

$\sqrt{\Delta}=\sqrt{2080}=\sqrt{16*130}=\sqrt{16}*\sqrt{130}=4\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{130}}{2*3}=\frac{4-4\sqrt{130}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{130}}{2*3}=\frac{4+4\sqrt{130}}{6}
$