6x^2+11x=65

Solution for 6x^2+11x=65 equation:

6x^2+11x=65

We move all terms to the left:

6x^2+11x-(65)=0

a = 6; b = 11; c = -65;
Δ = b2-4ac
Δ = 112-4·6·(-65)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-41}{2*6}=\frac{-52}{12}
=-4+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+41}{2*6}=\frac{30}{12}
=2+1/2
$