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

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

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

We move all terms to the left:

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


Domain of the equation: 2u!=0

u!=0/2

u!=0

u∈R



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

u∈R


We get rid of parentheses

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

We calculate fractions


32u^2/72u^2+(-180u)/72u^2+126u/72u^2+3=0

We multiply all the terms by the denominator


32u^2+(-180u)+126u+3*72u^2=0

We add all the numbers together, and all the variables

32u^2+126u+(-180u)+3*72u^2=0

Wy multiply elements

32u^2+216u^2+126u+(-180u)=0

We get rid of parentheses

32u^2+216u^2+126u-180u=0

We add all the numbers together, and all the variables

248u^2-54u=0

a = 248; b = -54; c = 0;
Δ = b2-4ac
Δ = -542-4·248·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-54}{2*248}=\frac{0}{496}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+54}{2*248}=\frac{108}{496}
=27/124
$