3/5x=40+2x/80x

Solution for 3/5x=40+2x/80x equation:

3/5x=40+2x/80x

We move all terms to the left:

3/5x-(40+2x/80x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 80x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-(2x/80x+40)=0

We get rid of parentheses

3/5x-2x/80x-40=0

We calculate fractions


(-10x^2)/400x^2+240x/400x^2-40=0

We multiply all the terms by the denominator


(-10x^2)+240x-40*400x^2=0

Wy multiply elements

(-10x^2)-16000x^2+240x=0

We get rid of parentheses

-10x^2-16000x^2+240x=0

We add all the numbers together, and all the variables

-16010x^2+240x=0

a = -16010; b = 240; c = 0;
Δ = b2-4ac
Δ = 2402-4·(-16010)·0
Δ = 57600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57600}=240$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-240}{2*-16010}=\frac{-480}{-32020}
=24/1601
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+240}{2*-16010}=\frac{0}{-32020}
=0
$