(92/X)-20+x=7

Solution for (92/X)-20+x=7 equation:

(92/X)-20+X=7

We move all terms to the left:

(92/X)-20+X-(7)=0


Domain of the equation: X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

(+92/X)+X-20-7=0

We add all the numbers together, and all the variables

X+(+92/X)-27=0

We get rid of parentheses

X+92/X-27=0

We multiply all the terms by the denominator


X*X-27*X+92=0

We add all the numbers together, and all the variables

-27X+X*X+92=0

Wy multiply elements

X^2-27X+92=0

a = 1; b = -27; c = +92;
Δ = b2-4ac
Δ = -272-4·1·92
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-19}{2*1}=\frac{8}{2}
=4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+19}{2*1}=\frac{46}{2}
=23
$