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

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

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

We move all terms to the left:

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


Domain of the equation: 2u!=0

u!=0/2

u!=0

u∈R



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

We move all terms containing u to the left, all other terms to the right

5u-2)!=5

u∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-25u)/10u^2+6u/10u^2+7+5=0

We add all the numbers together, and all the variables

(-25u)/10u^2+6u/10u^2+12=0

We multiply all the terms by the denominator


(-25u)+6u+12*10u^2=0

We add all the numbers together, and all the variables

6u+(-25u)+12*10u^2=0

Wy multiply elements

120u^2+6u+(-25u)=0

We get rid of parentheses

120u^2+6u-25u=0

We add all the numbers together, and all the variables

120u^2-19u=0

a = 120; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·120·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*120}=\frac{0}{240}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*120}=\frac{38}{240}
=19/120
$