6v^2-7v-10=-v^2

Solution for 6v^2-7v-10=-v^2 equation:

6v^2-7v-10=-v^2

We move all terms to the left:

6v^2-7v-10-(-v^2)=0

We get rid of parentheses

6v^2+v^2-7v-10=0

We add all the numbers together, and all the variables

7v^2-7v-10=0

a = 7; b = -7; c = -10;
Δ = b2-4ac
Δ = -72-4·7·(-10)
Δ = 329
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{329}}{2*7}=\frac{7-\sqrt{329}}{14}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{329}}{2*7}=\frac{7+\sqrt{329}}{14}
$