1/4x+5=1/10x+8

Solution for 1/4x+5=1/10x+8 equation:

1/4x+5=1/10x+8

We move all terms to the left:

1/4x+5-(1/10x+8)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 10x+8)!=0

x∈R


We get rid of parentheses

1/4x-1/10x-8+5=0

We calculate fractions


10x/40x^2+(-4x)/40x^2-8+5=0

We add all the numbers together, and all the variables

10x/40x^2+(-4x)/40x^2-3=0

We multiply all the terms by the denominator


10x+(-4x)-3*40x^2=0

Wy multiply elements

-120x^2+10x+(-4x)=0

We get rid of parentheses

-120x^2+10x-4x=0

We add all the numbers together, and all the variables

-120x^2+6x=0

a = -120; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-120)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-120}=\frac{-12}{-240}
=1/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-120}=\frac{0}{-240}
=0
$