12x^2-9x=18

Solution for 12x^2-9x=18 equation:

12x^2-9x=18

We move all terms to the left:

12x^2-9x-(18)=0

a = 12; b = -9; c = -18;
Δ = b2-4ac
Δ = -92-4·12·(-18)
Δ = 945
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:

$\sqrt{\Delta}=\sqrt{945}=\sqrt{9*105}=\sqrt{9}*\sqrt{105}=3\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{105}}{2*12}=\frac{9-3\sqrt{105}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{105}}{2*12}=\frac{9+3\sqrt{105}}{24}
$