7x^2-12x=9

Solution for 7x^2-12x=9 equation:

7x^2-12x=9

We move all terms to the left:

7x^2-12x-(9)=0

a = 7; b = -12; c = -9;
Δ = b2-4ac
Δ = -122-4·7·(-9)
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{11}}{2*7}=\frac{12-6\sqrt{11}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{11}}{2*7}=\frac{12+6\sqrt{11}}{14}
$