1/u-5=6/4u-6

Solution for 1/u-5=6/4u-6 equation:

1/u-5=6/4u-6

We move all terms to the left:

1/u-5-(6/4u-6)=0


Domain of the equation: u!=0

u∈R



Domain of the equation: 4u-6)!=0

u∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


4u+(-6u)+1*4u^2=0

Wy multiply elements

4u^2+4u+(-6u)=0

We get rid of parentheses

4u^2+4u-6u=0

We add all the numbers together, and all the variables

4u^2-2u=0

a = 4; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·4·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*4}=\frac{0}{8}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*4}=\frac{4}{8}
=1/2
$