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

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

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

We move all terms to the left:

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

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

We add all the numbers together, and all the variables

4v^2+7v-3=0

a = 4; b = 7; c = -3;
Δ = b2-4ac
Δ = 72-4·4·(-3)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{97}}{2*4}=\frac{-7-\sqrt{97}}{8}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{97}}{2*4}=\frac{-7+\sqrt{97}}{8}
$