5/3x-x=-40

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

5/3x-x=-40

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-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 = 14460
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:

$\sqrt{\Delta}=\sqrt{14460}=\sqrt{4*3615}=\sqrt{4}*\sqrt{3615}=2\sqrt{3615}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-2\sqrt{3615}}{2*-3}=\frac{-120-2\sqrt{3615}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+2\sqrt{3615}}{2*-3}=\frac{-120+2\sqrt{3615}}{-6}
$