4/x=5/4x+1

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

4/x=5/4x+1

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


16x/4x^2+(-5x)/4x^2-1=0

We multiply all the terms by the denominator


16x+(-5x)-1*4x^2=0

Wy multiply elements

-4x^2+16x+(-5x)=0

We get rid of parentheses

-4x^2+16x-5x=0

We add all the numbers together, and all the variables

-4x^2+11x=0

a = -4; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-4)·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*-4}=\frac{-22}{-8}
=2+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-4}=\frac{0}{-8}
=0
$