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

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

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

We move all terms to the left:

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


Domain of the equation: 2u!=0

u!=0/2

u!=0

u∈R



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

u∈R


We get rid of parentheses

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

We calculate fractions


(-25u)/40u^2+32u/40u^2+25u/40u^2+2=0

We multiply all the terms by the denominator


(-25u)+32u+25u+2*40u^2=0

We add all the numbers together, and all the variables

57u+(-25u)+2*40u^2=0

Wy multiply elements

80u^2+57u+(-25u)=0

We get rid of parentheses

80u^2+57u-25u=0

We add all the numbers together, and all the variables

80u^2+32u=0

a = 80; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·80·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*80}=\frac{-64}{160}
=-2/5
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*80}=\frac{0}{160}
=0
$