1/10x-1/4x=21

Solution for 1/10x-1/4x=21 equation:

1/10x-1/4x=21

We move all terms to the left:

1/10x-1/4x-(21)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


4x/40x^2+(-10x)/40x^2-21=0

We multiply all the terms by the denominator


4x+(-10x)-21*40x^2=0

Wy multiply elements

-840x^2+4x+(-10x)=0

We get rid of parentheses

-840x^2+4x-10x=0

We add all the numbers together, and all the variables

-840x^2-6x=0

a = -840; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-840)·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*-840}=\frac{0}{-1680}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-840}=\frac{12}{-1680}
=-1/140
$