-1/10+2/5x=-5/4x+1

Solution for -1/10+2/5x=-5/4x+1 equation:

-1/10+2/5x=-5/4x+1

We move all terms to the left:

-1/10+2/5x-(-5/4x+1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

2/5x+5/4x-1-1/10=0

We calculate fractions


(-80x^2)/200x^2+80x/200x^2+250x/200x^2-1=0

We multiply all the terms by the denominator


(-80x^2)+80x+250x-1*200x^2=0

We add all the numbers together, and all the variables

(-80x^2)+330x-1*200x^2=0

Wy multiply elements

(-80x^2)-200x^2+330x=0

We get rid of parentheses

-80x^2-200x^2+330x=0

We add all the numbers together, and all the variables

-280x^2+330x=0

a = -280; b = 330; c = 0;
Δ = b2-4ac
Δ = 3302-4·(-280)·0
Δ = 108900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{108900}=330$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(330)-330}{2*-280}=\frac{-660}{-560}
=1+5/28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(330)+330}{2*-280}=\frac{0}{-560}
=0
$