6v^2=-9v+15

Solution for 6v^2=-9v+15 equation:

6v^2=-9v+15

We move all terms to the left:

6v^2-(-9v+15)=0

We get rid of parentheses

6v^2+9v-15=0

a = 6; b = 9; c = -15;
Δ = b2-4ac
Δ = 92-4·6·(-15)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-21}{2*6}=\frac{-30}{12}
=-2+1/2
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+21}{2*6}=\frac{12}{12}
=1
$