9x2-3x=2

Solution for 9x2-3x=2 equation:

9x^2-3x=2

We move all terms to the left:

9x^2-3x-(2)=0

a = 9; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·9·(-2)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-9}{2*9}=\frac{-6}{18}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+9}{2*9}=\frac{12}{18}
=2/3
$