x-72/x=1

Solution for x-72/x=1 equation:

x-72/x=1

We move all terms to the left:

x-72/x-(1)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-1*x-72=0

We add all the numbers together, and all the variables

-1x+x*x-72=0

Wy multiply elements

x^2-1x-72=0

a = 1; b = -1; c = -72;
Δ = b2-4ac
Δ = -12-4·1·(-72)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-17}{2*1}=\frac{-16}{2}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+17}{2*1}=\frac{18}{2}
=9
$