9=v+4/v+12-13

Solution for 9=v+4/v+12-13 equation:

9=v+4/v+12-13

We move all terms to the left:

9-(v+4/v+12-13)=0


Domain of the equation: v+12-13)!=0

We move all terms containing v to the left, all other terms to the right

v-13)!=-12

v∈R


We add all the numbers together, and all the variables

-(v+4/v-1)+9=0

We get rid of parentheses

-v-4/v+1+9=0

We multiply all the terms by the denominator


-v*v+1*v+9*v-4=0

We add all the numbers together, and all the variables

10v-v*v-4=0

Wy multiply elements

-1v^2+10v-4=0

a = -1; b = 10; c = -4;
Δ = b2-4ac
Δ = 102-4·(-1)·(-4)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{21}}{2*-1}=\frac{-10-2\sqrt{21}}{-2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{21}}{2*-1}=\frac{-10+2\sqrt{21}}{-2}
$