v-9/10v=17

Solution for v-9/10v=17 equation:

v-9/10v=17

We move all terms to the left:

v-9/10v-(17)=0


Domain of the equation: 10v!=0

v!=0/10

v!=0

v∈R


We multiply all the terms by the denominator


v*10v-17*10v-9=0

Wy multiply elements

10v^2-170v-9=0

a = 10; b = -170; c = -9;
Δ = b2-4ac
Δ = -1702-4·10·(-9)
Δ = 29260
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:

$\sqrt{\Delta}=\sqrt{29260}=\sqrt{4*7315}=\sqrt{4}*\sqrt{7315}=2\sqrt{7315}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-170)-2\sqrt{7315}}{2*10}=\frac{170-2\sqrt{7315}}{20}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-170)+2\sqrt{7315}}{2*10}=\frac{170+2\sqrt{7315}}{20}
$