X-2/5x+21=x+1/8x

Solution for X-2/5x+21=x+1/8x equation:

X-2/5X+21=X+1/8X

We move all terms to the left:

X-2/5X+21-(X+1/8X)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R



Domain of the equation: 8X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-2/5X-(+X+1/8X)+21=0

We get rid of parentheses

X-2/5X-X-1/8X+21=0

We calculate fractions


X-X+(-16X)/40X^2+(-5X)/40X^2+21=0

We add all the numbers together, and all the variables

(-16X)/40X^2+(-5X)/40X^2+21=0

We multiply all the terms by the denominator


(-16X)+(-5X)+21*40X^2=0

Wy multiply elements

840X^2+(-16X)+(-5X)=0

We get rid of parentheses

840X^2-16X-5X=0

We add all the numbers together, and all the variables

840X^2-21X=0

a = 840; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·840·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*840}=\frac{0}{1680}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*840}=\frac{42}{1680}
=1/40
$