-v-9/10v+6=11

Solution for -v-9/10v+6=11 equation:

-v-9/10v+6=11

We move all terms to the left:

-v-9/10v+6-(11)=0


Domain of the equation: 10v!=0

v!=0/10

v!=0

v∈R


We add all the numbers together, and all the variables

-1v-9/10v-5=0

We multiply all the terms by the denominator


-1v*10v-5*10v-9=0

Wy multiply elements

-10v^2-50v-9=0

a = -10; b = -50; c = -9;
Δ = b2-4ac
Δ = -502-4·(-10)·(-9)
Δ = 2140
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:

$\sqrt{\Delta}=\sqrt{2140}=\sqrt{4*535}=\sqrt{4}*\sqrt{535}=2\sqrt{535}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{535}}{2*-10}=\frac{50-2\sqrt{535}}{-20}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{535}}{2*-10}=\frac{50+2\sqrt{535}}{-20}
$