6x^2-30x-36=11

Solution for 6x^2-30x-36=11 equation:

6x^2-30x-36=11

We move all terms to the left:

6x^2-30x-36-(11)=0

We add all the numbers together, and all the variables

6x^2-30x-47=0

a = 6; b = -30; c = -47;
Δ = b2-4ac
Δ = -302-4·6·(-47)
Δ = 2028
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:

$\sqrt{\Delta}=\sqrt{2028}=\sqrt{676*3}=\sqrt{676}*\sqrt{3}=26\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-26\sqrt{3}}{2*6}=\frac{30-26\sqrt{3}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+26\sqrt{3}}{2*6}=\frac{30+26\sqrt{3}}{12}
$