9x^2-14=12x

Solution for 9x^2-14=12x equation:

9x^2-14=12x

We move all terms to the left:

9x^2-14-(12x)=0

a = 9; b = -12; c = -14;
Δ = b2-4ac
Δ = -122-4·9·(-14)
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-18\sqrt{2}}{2*9}=\frac{12-18\sqrt{2}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+18\sqrt{2}}{2*9}=\frac{12+18\sqrt{2}}{18}
$