1=-10v+9v2

Solution for 1=-10v+9v2 equation:

1=-10v+9v^2

We move all terms to the left:

1-(-10v+9v^2)=0

We get rid of parentheses

-9v^2+10v+1=0

a = -9; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·(-9)·1
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{34}}{2*-9}=\frac{-10-2\sqrt{34}}{-18}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{34}}{2*-9}=\frac{-10+2\sqrt{34}}{-18}
$