5/7v-8=2+2v

Solution for 5/7v-8=2+2v equation:

5/7v-8=2+2v

We move all terms to the left:

5/7v-8-(2+2v)=0


Domain of the equation: 7v!=0

v!=0/7

v!=0

v∈R


We add all the numbers together, and all the variables

5/7v-(2v+2)-8=0

We get rid of parentheses

5/7v-2v-2-8=0

We multiply all the terms by the denominator


-2v*7v-2*7v-8*7v+5=0

Wy multiply elements

-14v^2-14v-56v+5=0

We add all the numbers together, and all the variables

-14v^2-70v+5=0

a = -14; b = -70; c = +5;
Δ = b2-4ac
Δ = -702-4·(-14)·5
Δ = 5180
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:

$\sqrt{\Delta}=\sqrt{5180}=\sqrt{4*1295}=\sqrt{4}*\sqrt{1295}=2\sqrt{1295}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1295}}{2*-14}=\frac{70-2\sqrt{1295}}{-28}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1295}}{2*-14}=\frac{70+2\sqrt{1295}}{-28}
$