5v+20-5/2v=35

Solution for 5v+20-5/2v=35 equation:

5v+20-5/2v=35

We move all terms to the left:

5v+20-5/2v-(35)=0


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R


We add all the numbers together, and all the variables

5v-5/2v-15=0

We multiply all the terms by the denominator


5v*2v-15*2v-5=0

Wy multiply elements

10v^2-30v-5=0

a = 10; b = -30; c = -5;
Δ = b2-4ac
Δ = -302-4·10·(-5)
Δ = 1100
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:

$\sqrt{\Delta}=\sqrt{1100}=\sqrt{100*11}=\sqrt{100}*\sqrt{11}=10\sqrt{11}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{11}}{2*10}=\frac{30-10\sqrt{11}}{20}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{11}}{2*10}=\frac{30+10\sqrt{11}}{20}
$