x/5x=40+3x

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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 $

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