40-5x=1/3x

Solution for 40-5x=1/3x equation:

40-5x=1/3x

We move all terms to the left:

40-5x-(1/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-5x-(+1/3x)+40=0

We get rid of parentheses

-5x-1/3x+40=0

We multiply all the terms by the denominator


-5x*3x+40*3x-1=0

Wy multiply elements

-15x^2+120x-1=0

a = -15; b = 120; c = -1;
Δ = b2-4ac
Δ = 1202-4·(-15)·(-1)
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*-15}=\frac{-120-2\sqrt{3585}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+2\sqrt{3585}}{2*-15}=\frac{-120+2\sqrt{3585}}{-30}
$