-5/8x-7/40x+1/5=-48

Solution for -5/8x-7/40x+1/5=-48 equation:

-5/8x-7/40x+1/5=-48

We move all terms to the left:

-5/8x-7/40x+1/5-(-48)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 40x!=0

x!=0/40

x!=0

x∈R


We add all the numbers together, and all the variables

-5/8x-7/40x+48+1/5=0

We calculate fractions


1280x^2/8000x^2+(-5000x)/8000x^2+(-1400x)/8000x^2+48=0

We multiply all the terms by the denominator


1280x^2+(-5000x)+(-1400x)+48*8000x^2=0

Wy multiply elements

1280x^2+384000x^2+(-5000x)+(-1400x)=0

We get rid of parentheses

1280x^2+384000x^2-5000x-1400x=0

We add all the numbers together, and all the variables

385280x^2-6400x=0

a = 385280; b = -6400; c = 0;
Δ = b2-4ac
Δ = -64002-4·385280·0
Δ = 40960000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40960000}=6400$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6400)-6400}{2*385280}=\frac{0}{770560}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6400)+6400}{2*385280}=\frac{12800}{770560}
=5/301
$