-v-5/2v=7

Solution for -v-5/2v=7 equation:

-v-5/2v=7

We move all terms to the left:

-v-5/2v-(7)=0


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R


We add all the numbers together, and all the variables

-1v-5/2v-7=0

We multiply all the terms by the denominator


-1v*2v-7*2v-5=0

Wy multiply elements

-2v^2-14v-5=0

a = -2; b = -14; c = -5;
Δ = b2-4ac
Δ = -142-4·(-2)·(-5)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{39}}{2*-2}=\frac{14-2\sqrt{39}}{-4}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{39}}{2*-2}=\frac{14+2\sqrt{39}}{-4}
$