v-8=1/53v-8

Solution for v-8=1/53v-8 equation:

v-8=1/53v-8

We move all terms to the left:

v-8-(1/53v-8)=0


Domain of the equation: 53v-8)!=0

v∈R


We get rid of parentheses

v-1/53v+8-8=0

We multiply all the terms by the denominator


v*53v+8*53v-8*53v-1=0

Wy multiply elements

53v^2+424v-424v-1=0

We add all the numbers together, and all the variables

53v^2-1=0

a = 53; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·53·(-1)
Δ = 212
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:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{53}}{2*53}=\frac{0-2\sqrt{53}}{106}
=-\frac{2\sqrt{53}}{106}
=-\frac{\sqrt{53}}{53}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{53}}{2*53}=\frac{0+2\sqrt{53}}{106}
=\frac{2\sqrt{53}}{106}
=\frac{\sqrt{53}}{53}
$