6x^2-6=19x

Solution for 6x^2-6=19x equation:

6x^2-6=19x

We move all terms to the left:

6x^2-6-(19x)=0

a = 6; b = -19; c = -6;
Δ = b2-4ac
Δ = -192-4·6·(-6)
Δ = 505
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{505}}{2*6}=\frac{19-\sqrt{505}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{505}}{2*6}=\frac{19+\sqrt{505}}{12}
$