-(1/2u-12)+4=5/u-6

Solution for -(1/2u-12)+4=5/u-6 equation:

-(1/2u-12)+4=5/u-6

We move all terms to the left:

-(1/2u-12)+4-(5/u-6)=0


Domain of the equation: 2u-12)!=0

u∈R



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

u∈R


We get rid of parentheses

-1/2u-5/u+12+6+4=0

We calculate fractions


(-u)/2u^2+(-10u)/2u^2+12+6+4=0

We add all the numbers together, and all the variables

(-1u)/2u^2+(-10u)/2u^2+12+6+4=0

We add all the numbers together, and all the variables

(-1u)/2u^2+(-10u)/2u^2+22=0

We multiply all the terms by the denominator


(-1u)+(-10u)+22*2u^2=0

Wy multiply elements

44u^2+(-1u)+(-10u)=0

We get rid of parentheses

44u^2-1u-10u=0

We add all the numbers together, and all the variables

44u^2-11u=0

a = 44; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·44·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*44}=\frac{0}{88}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*44}=\frac{22}{88}
=1/4
$