6v^2-15v+2=3v^2-9v+10

Solution for 6v^2-15v+2=3v^2-9v+10 equation:

6v^2-15v+2=3v^2-9v+10

We move all terms to the left:

6v^2-15v+2-(3v^2-9v+10)=0

We get rid of parentheses

6v^2-3v^2-15v+9v-10+2=0

We add all the numbers together, and all the variables

3v^2-6v-8=0

a = 3; b = -6; c = -8;
Δ = b2-4ac
Δ = -62-4·3·(-8)
Δ = 132
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{33}}{2*3}=\frac{6-2\sqrt{33}}{6}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{33}}{2*3}=\frac{6+2\sqrt{33}}{6}
$