2x^2+9=12x

Solution for 2x^2+9=12x equation:

2x^2+9=12x

We move all terms to the left:

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

a = 2; b = -12; c = +9;
Δ = b2-4ac
Δ = -122-4·2·9
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{2}}{2*2}=\frac{12-6\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{2}}{2*2}=\frac{12+6\sqrt{2}}{4}
$