-7/3u+3/4=-1/2u-5

Solution for -7/3u+3/4=-1/2u-5 equation:

-7/3u+3/4=-1/2u-5

We move all terms to the left:

-7/3u+3/4-(-1/2u-5)=0


Domain of the equation: 3u!=0

u!=0/3

u!=0

u∈R



Domain of the equation: 2u-5)!=0

u∈R


We get rid of parentheses

-7/3u+1/2u+5+3/4=0

We calculate fractions


36u^2/96u^2+(-224u)/96u^2+48u/96u^2+5=0

We multiply all the terms by the denominator


36u^2+(-224u)+48u+5*96u^2=0

We add all the numbers together, and all the variables

36u^2+48u+(-224u)+5*96u^2=0

Wy multiply elements

36u^2+480u^2+48u+(-224u)=0

We get rid of parentheses

36u^2+480u^2+48u-224u=0

We add all the numbers together, and all the variables

516u^2-176u=0

a = 516; b = -176; c = 0;
Δ = b2-4ac
Δ = -1762-4·516·0
Δ = 30976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{30976}=176$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-176)-176}{2*516}=\frac{0}{1032}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-176)+176}{2*516}=\frac{352}{1032}
=44/129
$