14-28/v=v+25

Solution for 14-28/v=v+25 equation:

14-28/v=v+25

We move all terms to the left:

14-28/v-(v+25)=0


Domain of the equation: v!=0

v∈R


We get rid of parentheses

-28/v-v-25+14=0

We multiply all the terms by the denominator


-v*v-25*v+14*v-28=0

We add all the numbers together, and all the variables

-11v-v*v-28=0

Wy multiply elements

-1v^2-11v-28=0

a = -1; b = -11; c = -28;
Δ = b2-4ac
Δ = -112-4·(-1)·(-28)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-3}{2*-1}=\frac{8}{-2}
=-4
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3}{2*-1}=\frac{14}{-2}
=-7
$