(1/u+1)+5=3/4u+3

Solution for (1/u+1)+5=3/4u+3 equation:

(1/u+1)+5=3/4u+3

We move all terms to the left:

(1/u+1)+5-(3/4u+3)=0


Domain of the equation: u+1)!=0

u∈R



Domain of the equation: 4u+3)!=0

u∈R


We get rid of parentheses

1/u-3/4u+1-3+5=0

We calculate fractions


4u/4u^2+(-3u)/4u^2+1-3+5=0

We add all the numbers together, and all the variables

4u/4u^2+(-3u)/4u^2+3=0

We multiply all the terms by the denominator


4u+(-3u)+3*4u^2=0

Wy multiply elements

12u^2+4u+(-3u)=0

We get rid of parentheses

12u^2+4u-3u=0

We add all the numbers together, and all the variables

12u^2+u=0

a = 12; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·12·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*12}=\frac{-2}{24}
=-1/12
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*12}=\frac{0}{24}
=0
$