6x^2-52=11x

Solution for 6x^2-52=11x equation:

6x^2-52=11x

We move all terms to the left:

6x^2-52-(11x)=0

a = 6; b = -11; c = -52;
Δ = b2-4ac
Δ = -112-4·6·(-52)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-37}{2*6}=\frac{-26}{12}
=-2+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+37}{2*6}=\frac{48}{12}
=4
$