-3/2u-7/2=4/3u-7

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

-3/2u-7/2=4/3u-7

We move all terms to the left:

-3/2u-7/2-(4/3u-7)=0


Domain of the equation: 2u!=0

u!=0/2

u!=0

u∈R



Domain of the equation: 3u-7)!=0

u∈R


We get rid of parentheses

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

We calculate fractions


(-9u)/24u^2+(-32u)/24u^2+(-21u)/24u^2+7=0

We multiply all the terms by the denominator


(-9u)+(-32u)+(-21u)+7*24u^2=0

Wy multiply elements

168u^2+(-9u)+(-32u)+(-21u)=0

We get rid of parentheses

168u^2-9u-32u-21u=0

We add all the numbers together, and all the variables

168u^2-62u=0

a = 168; b = -62; c = 0;
Δ = b2-4ac
Δ = -622-4·168·0
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-62)-62}{2*168}=\frac{0}{336}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-62)+62}{2*168}=\frac{124}{336}
=31/84
$