48-x=1/5xX

Solution for 48-x=1/5xX equation:

48-x=1/5xx

We move all terms to the left:

48-x-(1/5xx)=0


Domain of the equation: 5xx)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-x-(+1/5xx)+48=0

We add all the numbers together, and all the variables

-1x-(+1/5xx)+48=0

We get rid of parentheses

-1x-1/5xx+48=0

We multiply all the terms by the denominator


-1x*5xx+48*5xx-1=0

Wy multiply elements

-5x^2+240x-1=0

a = -5; b = 240; c = -1;
Δ = b2-4ac
Δ = 2402-4·(-5)·(-1)
Δ = 57580
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:

$\sqrt{\Delta}=\sqrt{57580}=\sqrt{4*14395}=\sqrt{4}*\sqrt{14395}=2\sqrt{14395}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-2\sqrt{14395}}{2*-5}=\frac{-240-2\sqrt{14395}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+2\sqrt{14395}}{2*-5}=\frac{-240+2\sqrt{14395}}{-10}
$