X=72+1/7x

Solution for X=72+1/7x equation:

X=72+1/7X

We move all terms to the left:

X-(72+1/7X)=0


Domain of the equation: 7X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(1/7X+72)=0

We get rid of parentheses

X-1/7X-72=0

We multiply all the terms by the denominator


X*7X-72*7X-1=0

Wy multiply elements

7X^2-504X-1=0

a = 7; b = -504; c = -1;
Δ = b2-4ac
Δ = -5042-4·7·(-1)
Δ = 254044
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:

$\sqrt{\Delta}=\sqrt{254044}=\sqrt{4*63511}=\sqrt{4}*\sqrt{63511}=2\sqrt{63511}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-504)-2\sqrt{63511}}{2*7}=\frac{504-2\sqrt{63511}}{14}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-504)+2\sqrt{63511}}{2*7}=\frac{504+2\sqrt{63511}}{14}
$