V=22v-5/4v-8

Solution for V=22v-5/4v-8 equation:

=22V-5/4V-8

We move all terms to the left:

-(22V-5/4V-8)=0


Domain of the equation: 4V-8)!=0

V∈R


We get rid of parentheses

-22V+5/4V+8=0

We multiply all the terms by the denominator


-22V*4V+8*4V+5=0

Wy multiply elements

-88V^2+32V+5=0

a = -88; b = 32; c = +5;
Δ = b2-4ac
Δ = 322-4·(-88)·5
Δ = 2784
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:

$\sqrt{\Delta}=\sqrt{2784}=\sqrt{16*174}=\sqrt{16}*\sqrt{174}=4\sqrt{174}$
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{174}}{2*-88}=\frac{-32-4\sqrt{174}}{-176}
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{174}}{2*-88}=\frac{-32+4\sqrt{174}}{-176}
$