3x^2-11=12x

Solution for 3x^2-11=12x equation:

3x^2-11=12x

We move all terms to the left:

3x^2-11-(12x)=0

a = 3; b = -12; c = -11;
Δ = b2-4ac
Δ = -122-4·3·(-11)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{69}}{2*3}=\frac{12-2\sqrt{69}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{69}}{2*3}=\frac{12+2\sqrt{69}}{6}
$