5v^2+7v-3=v-v^2

Solution for 5v^2+7v-3=v-v^2 equation:

5v^2+7v-3=v-v^2

We move all terms to the left:

5v^2+7v-3-(v-v^2)=0

We get rid of parentheses

5v^2+v^2-v+7v-3=0

We add all the numbers together, and all the variables

6v^2+6v-3=0

a = 6; b = 6; c = -3;
Δ = b2-4ac
Δ = 62-4·6·(-3)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{3}}{2*6}=\frac{-6-6\sqrt{3}}{12}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{3}}{2*6}=\frac{-6+6\sqrt{3}}{12}
$