40-x=5/3x

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



40-x=5/3x
We move all terms to the left:
40-x-(5/3x)=0
Domain of the equation: 3x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
-x-(+5/3x)+40=0
We add all the numbers together, and all the variables
-1x-(+5/3x)+40=0
We get rid of parentheses
-1x-5/3x+40=0
We multiply all the terms by the denominator
-1x*3x+40*3x-5=0
Wy multiply elements
-3x^2+120x-5=0
a = -3; b = 120; c = -5;
Δ = b2-4ac
Δ = 1202-4·(-3)·(-5)
Δ = 14340
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{14340}=\sqrt{4*3585}=\sqrt{4}*\sqrt{3585}=2\sqrt{3585}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-2\sqrt{3585}}{2*-3}=\frac{-120-2\sqrt{3585}}{-6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+2\sqrt{3585}}{2*-3}=\frac{-120+2\sqrt{3585}}{-6} $

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