17v^2+8v+1=8v^2-3v

Solution for 17v^2+8v+1=8v^2-3v equation:

17v^2+8v+1=8v^2-3v

We move all terms to the left:

17v^2+8v+1-(8v^2-3v)=0

We get rid of parentheses

17v^2-8v^2+8v+3v+1=0

We add all the numbers together, and all the variables

9v^2+11v+1=0

a = 9; b = 11; c = +1;
Δ = b2-4ac
Δ = 112-4·9·1
Δ = 85
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{-(11)-\sqrt{85}}{2*9}=\frac{-11-\sqrt{85}}{18}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{85}}{2*9}=\frac{-11+\sqrt{85}}{18}
$