1/5x=24-x

Solution for 1/5x=24-x equation:

1/5x=24-x

We move all terms to the left:

1/5x-(24-x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

1/5x-(-1x+24)=0

We get rid of parentheses

1/5x+1x-24=0

We multiply all the terms by the denominator


1x*5x-24*5x+1=0

Wy multiply elements

5x^2-120x+1=0

a = 5; b = -120; c = +1;
Δ = b2-4ac
Δ = -1202-4·5·1
Δ = 14380
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:

$\sqrt{\Delta}=\sqrt{14380}=\sqrt{4*3595}=\sqrt{4}*\sqrt{3595}=2\sqrt{3595}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-2\sqrt{3595}}{2*5}=\frac{120-2\sqrt{3595}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+2\sqrt{3595}}{2*5}=\frac{120+2\sqrt{3595}}{10}
$