-5/2u-5/4=2/3u-3

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

-5/2u-5/4=2/3u-3

We move all terms to the left:

-5/2u-5/4-(2/3u-3)=0


Domain of the equation: 2u!=0

u!=0/2

u!=0

u∈R



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

u∈R


We get rid of parentheses

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

We calculate fractions


(-90u^2)/96u^2+(-240u)/96u^2+(-64u)/96u^2+3=0

We multiply all the terms by the denominator


(-90u^2)+(-240u)+(-64u)+3*96u^2=0

Wy multiply elements

(-90u^2)+288u^2+(-240u)+(-64u)=0

We get rid of parentheses

-90u^2+288u^2-240u-64u=0

We add all the numbers together, and all the variables

198u^2-304u=0

a = 198; b = -304; c = 0;
Δ = b2-4ac
Δ = -3042-4·198·0
Δ = 92416
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{92416}=304$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-304)-304}{2*198}=\frac{0}{396}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-304)+304}{2*198}=\frac{608}{396}
=1+53/99
$