6x^2+11x=19

Solution for 6x^2+11x=19 equation:

6x^2+11x=19

We move all terms to the left:

6x^2+11x-(19)=0

a = 6; b = 11; c = -19;
Δ = b2-4ac
Δ = 112-4·6·(-19)
Δ = 577
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{-(11)-\sqrt{577}}{2*6}=\frac{-11-\sqrt{577}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{577}}{2*6}=\frac{-11+\sqrt{577}}{12}
$