V+1/v-7+1=v-7/v-4

Solution for V+1/v-7+1=v-7/v-4 equation:

+1/V-7+1=V-7/V-4

We move all terms to the left:

+1/V-7+1-(V-7/V-4)=0


Domain of the equation: V!=0

V∈R



Domain of the equation: V-4)!=0

V∈R


We add all the numbers together, and all the variables

1/V-(V-7/V-4)-6=0

We get rid of parentheses

1/V-V+7/V+4-6=0

We multiply all the terms by the denominator


-V*V+4*V-6*V+1+7=0

We add all the numbers together, and all the variables

-2V-V*V+8=0

Wy multiply elements

-1V^2-2V+8=0

a = -1; b = -2; c = +8;
Δ = b2-4ac
Δ = -22-4·(-1)·8
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6}{2*-1}=\frac{-4}{-2}
=+2
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6}{2*-1}=\frac{8}{-2}
=-4
$