4/4x-3=-5/5x=1

Solution for 4/4x-3=-5/5x=1 equation:

4/4x-3=-5/5x=1

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

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

We calculate fractions


20x/20x^2+20x/20x^2-3=0

We multiply all the terms by the denominator


20x+20x-3*20x^2=0

We add all the numbers together, and all the variables

40x-3*20x^2=0

Wy multiply elements

-60x^2+40x=0

a = -60; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·(-60)·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*-60}=\frac{-80}{-120}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*-60}=\frac{0}{-120}
=0
$