4/5x=1/4x+2

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

4/5x=1/4x+2

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x+2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


16x+(-5x)-2*20x^2=0

Wy multiply elements

-40x^2+16x+(-5x)=0

We get rid of parentheses

-40x^2+16x-5x=0

We add all the numbers together, and all the variables

-40x^2+11x=0

a = -40; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-40)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-40}=\frac{-22}{-80}
=11/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-40}=\frac{0}{-80}
=0
$