v-1=3/8v

Solution for v-1=3/8v equation:

v-1=3/8v

We move all terms to the left:

v-1-(3/8v)=0


Domain of the equation: 8v)!=0

v!=0/1

v!=0

v∈R


We add all the numbers together, and all the variables

v-(+3/8v)-1=0

We get rid of parentheses

v-3/8v-1=0

We multiply all the terms by the denominator


v*8v-1*8v-3=0

Wy multiply elements

8v^2-8v-3=0

a = 8; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·8·(-3)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{10}}{2*8}=\frac{8-4\sqrt{10}}{16}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{10}}{2*8}=\frac{8+4\sqrt{10}}{16}
$