1/5x-1/8x+1/40=5

Solution for 1/5x-1/8x+1/40=5 equation:

1/5x-1/8x+1/40=5

We move all terms to the left:

1/5x-1/8x+1/40-(5)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


determiningTheFunctionDomain
1/5x-1/8x-5+1/40=0

We calculate fractions


320x^2/6400x^2+1280x/6400x^2+(-800x)/6400x^2-5=0

We multiply all the terms by the denominator


320x^2+1280x+(-800x)-5*6400x^2=0

Wy multiply elements

320x^2-32000x^2+1280x+(-800x)=0

We get rid of parentheses

320x^2-32000x^2+1280x-800x=0

We add all the numbers together, and all the variables

-31680x^2+480x=0

a = -31680; b = 480; c = 0;
Δ = b2-4ac
Δ = 4802-4·(-31680)·0
Δ = 230400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{230400}=480$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(480)-480}{2*-31680}=\frac{-960}{-63360}
=1/66
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(480)+480}{2*-31680}=\frac{0}{-63360}
=0
$