6v^2-56=11v+9

Solution for 6v^2-56=11v+9 equation:

6v^2-56=11v+9

We move all terms to the left:

6v^2-56-(11v+9)=0

We get rid of parentheses

6v^2-11v-9-56=0

We add all the numbers together, and all the variables

6v^2-11v-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:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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