18x^2-9x=2

Solution for 18x^2-9x=2 equation:

18x^2-9x=2

We move all terms to the left:

18x^2-9x-(2)=0

a = 18; b = -9; c = -2;
Δ = b2-4ac
Δ = -92-4·18·(-2)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-15}{2*18}=\frac{-6}{36}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+15}{2*18}=\frac{24}{36}
=2/3
$