-5/2x-3=4/5x-5

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

-5/2x-3=4/5x-5

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x-5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-25x)/10x^2+(-8x)/10x^2+5-3=0

We add all the numbers together, and all the variables

(-25x)/10x^2+(-8x)/10x^2+2=0

We multiply all the terms by the denominator


(-25x)+(-8x)+2*10x^2=0

Wy multiply elements

20x^2+(-25x)+(-8x)=0

We get rid of parentheses

20x^2-25x-8x=0

We add all the numbers together, and all the variables

20x^2-33x=0

a = 20; b = -33; c = 0;
Δ = b2-4ac
Δ = -332-4·20·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-33}{2*20}=\frac{0}{40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+33}{2*20}=\frac{66}{40}
=1+13/20
$