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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


16x/20x^2+(-25x)/20x^2-3-5=0

We add all the numbers together, and all the variables

16x/20x^2+(-25x)/20x^2-8=0

We multiply all the terms by the denominator


16x+(-25x)-8*20x^2=0

Wy multiply elements

-160x^2+16x+(-25x)=0

We get rid of parentheses

-160x^2+16x-25x=0

We add all the numbers together, and all the variables

-160x^2-9x=0

a = -160; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-160)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-160}=\frac{0}{-320}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-160}=\frac{18}{-320}
=-9/160
$