-3v2+8v-1=-4v2-1

Solution for -3v2+8v-1=-4v2-1 equation:

-3v^2+8v-1=-4v^2-1

We move all terms to the left:

-3v^2+8v-1-(-4v^2-1)=0

We get rid of parentheses

-3v^2+4v^2+8v+1-1=0

We add all the numbers together, and all the variables

v^2+8v=0

a = 1; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·1·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*1}=\frac{-16}{2}
=-8
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*1}=\frac{0}{2}
=0
$