1/4x-2=1/5x+3

Solution for 1/4x-2=1/5x+3 equation:

1/4x-2=1/5x+3

We move all terms to the left:

1/4x-2-(1/5x+3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x+3)!=0

x∈R


We get rid of parentheses

1/4x-1/5x-3-2=0

We calculate fractions


5x/20x^2+(-4x)/20x^2-3-2=0

We add all the numbers together, and all the variables

5x/20x^2+(-4x)/20x^2-5=0

We multiply all the terms by the denominator


5x+(-4x)-5*20x^2=0

Wy multiply elements

-100x^2+5x+(-4x)=0

We get rid of parentheses

-100x^2+5x-4x=0

We add all the numbers together, and all the variables

-100x^2+x=0

a = -100; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-100)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-100}=\frac{-2}{-200}
=1/100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-100}=\frac{0}{-200}
=0
$