-7/2u-12+1=-7/u-6

Solution for -7/2u-12+1=-7/u-6 equation:

-7/2u-12+1=-7/u-6

We move all terms to the left:

-7/2u-12+1-(-7/u-6)=0


Domain of the equation: 2u!=0

u!=0/2

u!=0

u∈R



Domain of the equation: u-6)!=0

u∈R


We add all the numbers together, and all the variables

-7/2u-(-7/u-6)-11=0

We get rid of parentheses

-7/2u+7/u+6-11=0

We calculate fractions


(-7u)/2u^2+14u/2u^2+6-11=0

We add all the numbers together, and all the variables

(-7u)/2u^2+14u/2u^2-5=0

We multiply all the terms by the denominator


(-7u)+14u-5*2u^2=0

We add all the numbers together, and all the variables

14u+(-7u)-5*2u^2=0

Wy multiply elements

-10u^2+14u+(-7u)=0

We get rid of parentheses

-10u^2+14u-7u=0

We add all the numbers together, and all the variables

-10u^2+7u=0

a = -10; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-10)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-10}=\frac{-14}{-20}
=7/10
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-10}=\frac{0}{-20}
=0
$