3x^2-2x=89

Solution for 3x^2-2x=89 equation:

3x^2-2x=89

We move all terms to the left:

3x^2-2x-(89)=0

a = 3; b = -2; c = -89;
Δ = b2-4ac
Δ = -22-4·3·(-89)
Δ = 1072
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:

$\sqrt{\Delta}=\sqrt{1072}=\sqrt{16*67}=\sqrt{16}*\sqrt{67}=4\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{67}}{2*3}=\frac{2-4\sqrt{67}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{67}}{2*3}=\frac{2+4\sqrt{67}}{6}
$