5v^2=11v-2

Solution for 5v^2=11v-2 equation:

5v^2=11v-2

We move all terms to the left:

5v^2-(11v-2)=0

We get rid of parentheses

5v^2-11v+2=0

a = 5; b = -11; c = +2;
Δ = b2-4ac
Δ = -112-4·5·2
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-9}{2*5}=\frac{2}{10}
=1/5
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+9}{2*5}=\frac{20}{10}
=2
$