-1/7v+2.8=1.4v-3.1v+2.8

Solution for -1/7v+2.8=1.4v-3.1v+2.8 equation:

-1/7v+2.8=1.4v-3.1v+2.8

We move all terms to the left:

-1/7v+2.8-(1.4v-3.1v+2.8)=0


Domain of the equation: 7v!=0

v!=0/7

v!=0

v∈R


We add all the numbers together, and all the variables

-1/7v-(-1.7v+2.8)+2.8=0

We get rid of parentheses

-1/7v+1.7v-2.8+2.8=0

We multiply all the terms by the denominator


(1.7v)*7v-(2.8)*7v+(2.8)*7v-1=0

We add all the numbers together, and all the variables

(+1.7v)*7v-(2.8)*7v+(2.8)*7v-1=0

We multiply parentheses

7v^2-19.6v+19.6v-1=0

We add all the numbers together, and all the variables

7v^2-1=0

a = 7; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·7·(-1)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{7}}{2*7}=\frac{0-2\sqrt{7}}{14}
=-\frac{2\sqrt{7}}{14}
=-\frac{\sqrt{7}}{7}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{7}}{2*7}=\frac{0+2\sqrt{7}}{14}
=\frac{2\sqrt{7}}{14}
=\frac{\sqrt{7}}{7}
$