1/4x+5=1/5x+16

Solution for 1/4x+5=1/5x+16 equation:

1/4x+5=1/5x+16

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x+16)!=0

x∈R


We get rid of parentheses

1/4x-1/5x-16+5=0

We calculate fractions


5x/20x^2+(-4x)/20x^2-16+5=0

We add all the numbers together, and all the variables

5x/20x^2+(-4x)/20x^2-11=0

We multiply all the terms by the denominator


5x+(-4x)-11*20x^2=0

Wy multiply elements

-220x^2+5x+(-4x)=0

We get rid of parentheses

-220x^2+5x-4x=0

We add all the numbers together, and all the variables

-220x^2+x=0

a = -220; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-220)·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*-220}=\frac{-2}{-440}
=1/220
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-220}=\frac{0}{-440}
=0
$