6x2-9x=12

Solution for 6x2-9x=12 equation:

6x^2-9x=12

We move all terms to the left:

6x^2-9x-(12)=0

a = 6; b = -9; c = -12;
Δ = b2-4ac
Δ = -92-4·6·(-12)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{41}}{2*6}=\frac{9-3\sqrt{41}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{41}}{2*6}=\frac{9+3\sqrt{41}}{12}
$