1/3x=x-40

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

1/3x=x-40

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-x+40=0

We multiply all the terms by the denominator


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

Wy multiply elements

-3x^2+120x+1=0

a = -3; b = 120; c = +1;
Δ = b2-4ac
Δ = 1202-4·(-3)·1
Δ = 14412
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:

$\sqrt{\Delta}=\sqrt{14412}=\sqrt{4*3603}=\sqrt{4}*\sqrt{3603}=2\sqrt{3603}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-2\sqrt{3603}}{2*-3}=\frac{-120-2\sqrt{3603}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+2\sqrt{3603}}{2*-3}=\frac{-120+2\sqrt{3603}}{-6}
$