-2v^2-10v=-v^2-75

Solution for -2v^2-10v=-v^2-75 equation:

-2v^2-10v=-v^2-75

We move all terms to the left:

-2v^2-10v-(-v^2-75)=0

We get rid of parentheses

-2v^2+v^2-10v+75=0

We add all the numbers together, and all the variables

-1v^2-10v+75=0

a = -1; b = -10; c = +75;
Δ = b2-4ac
Δ = -102-4·(-1)·75
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-20}{2*-1}=\frac{-10}{-2}
=+5
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+20}{2*-1}=\frac{30}{-2}
=-15
$