v-9/10v=5

Solution for v-9/10v=5 equation:

v-9/10v=5

We move all terms to the left:

v-9/10v-(5)=0


Domain of the equation: 10v!=0

v!=0/10

v!=0

v∈R


We multiply all the terms by the denominator


v*10v-5*10v-9=0

Wy multiply elements

10v^2-50v-9=0

a = 10; b = -50; c = -9;
Δ = b2-4ac
Δ = -502-4·10·(-9)
Δ = 2860
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:

$\sqrt{\Delta}=\sqrt{2860}=\sqrt{4*715}=\sqrt{4}*\sqrt{715}=2\sqrt{715}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{715}}{2*10}=\frac{50-2\sqrt{715}}{20}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{715}}{2*10}=\frac{50+2\sqrt{715}}{20}
$