142/5+3/5x=48-4/8x

Solution for 142/5+3/5x=48-4/8x equation:

142/5+3/5x=48-4/8x

We move all terms to the left:

142/5+3/5x-(48-4/8x)=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

3/5x-(-4/8x+48)+142/5=0

We get rid of parentheses

3/5x+4/8x-48+142/5=0

We calculate fractions


24x/1000x^2+500x/1000x^2+1136x/1000x^2-48=0

We multiply all the terms by the denominator


24x+500x+1136x-48*1000x^2=0

We add all the numbers together, and all the variables

1660x-48*1000x^2=0

Wy multiply elements

-48000x^2+1660x=0

a = -48000; b = 1660; c = 0;
Δ = b2-4ac
Δ = 16602-4·(-48000)·0
Δ = 2755600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2755600}=1660$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1660)-1660}{2*-48000}=\frac{-3320}{-96000}
=83/2400
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1660)+1660}{2*-48000}=\frac{0}{-96000}
=0
$