15+1/4x=20+1/20x

Solution for 15+1/4x=20+1/20x equation:

15+1/4x=20+1/20x

We move all terms to the left:

15+1/4x-(20+1/20x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 20x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x-(1/20x+20)+15=0

We get rid of parentheses

1/4x-1/20x-20+15=0

We calculate fractions


20x/80x^2+(-4x)/80x^2-20+15=0

We add all the numbers together, and all the variables

20x/80x^2+(-4x)/80x^2-5=0

We multiply all the terms by the denominator


20x+(-4x)-5*80x^2=0

Wy multiply elements

-400x^2+20x+(-4x)=0

We get rid of parentheses

-400x^2+20x-4x=0

We add all the numbers together, and all the variables

-400x^2+16x=0

a = -400; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-400)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-400}=\frac{-32}{-800}
=1/25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-400}=\frac{0}{-800}
=0
$