x/5x=40+3x

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

x/5x=40+3x

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x/5x-3x-40=0

We multiply all the terms by the denominator


x-3x*5x-40*5x=0

Wy multiply elements

-15x^2+x-200x=0

We add all the numbers together, and all the variables

-15x^2-199x=0

a = -15; b = -199; c = 0;
Δ = b2-4ac
Δ = -1992-4·(-15)·0
Δ = 39601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{39601}=199$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-199)-199}{2*-15}=\frac{0}{-30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-199)+199}{2*-15}=\frac{398}{-30}
=-13+4/15
$