14/15v-5/6=8/9v-3

Solution for 14/15v-5/6=8/9v-3 equation:

14/15v-5/6=8/9v-3

We move all terms to the left:

14/15v-5/6-(8/9v-3)=0


Domain of the equation: 15v!=0

v!=0/15

v!=0

v∈R



Domain of the equation: 9v-3)!=0

v∈R


We get rid of parentheses

14/15v-8/9v+3-5/6=0

We calculate fractions


(-6075v^2)/4860v^2+4536v/4860v^2+(-4320v)/4860v^2+3=0

We multiply all the terms by the denominator


(-6075v^2)+4536v+(-4320v)+3*4860v^2=0

Wy multiply elements

(-6075v^2)+14580v^2+4536v+(-4320v)=0

We get rid of parentheses

-6075v^2+14580v^2+4536v-4320v=0

We add all the numbers together, and all the variables

8505v^2+216v=0

a = 8505; b = 216; c = 0;
Δ = b2-4ac
Δ = 2162-4·8505·0
Δ = 46656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{46656}=216$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(216)-216}{2*8505}=\frac{-432}{17010}
=-8/315
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(216)+216}{2*8505}=\frac{0}{17010}
=0
$