10v^2=9+8v

Solution for 10v^2=9+8v equation:

10v^2=9+8v

We move all terms to the left:

10v^2-(9+8v)=0

We add all the numbers together, and all the variables

10v^2-(8v+9)=0

We get rid of parentheses

10v^2-8v-9=0

a = 10; b = -8; c = -9;
Δ = b2-4ac
Δ = -82-4·10·(-9)
Δ = 424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{106}}{2*10}=\frac{8-2\sqrt{106}}{20}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{106}}{2*10}=\frac{8+2\sqrt{106}}{20}
$