(X-2)+(X-1)/x=720

Solution for (X-2)+(X-1)/x=720 equation:

(X-2)+(X-1)/X=720

We move all terms to the left:

(X-2)+(X-1)/X-(720)=0


Domain of the equation: X!=0

X∈R


We get rid of parentheses

X+(X-1)/X-2-720=0

We multiply all the terms by the denominator


X*X+(X-1)-2*X-720*X=0

We add all the numbers together, and all the variables

-722X+X*X+(X-1)=0

Wy multiply elements

X^2-722X+(X-1)=0

We get rid of parentheses

X^2-722X+X-1=0

We add all the numbers together, and all the variables

X^2-721X-1=0

a = 1; b = -721; c = -1;
Δ = b2-4ac
Δ = -7212-4·1·(-1)
Δ = 519845
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-721)-\sqrt{519845}}{2*1}=\frac{721-\sqrt{519845}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-721)+\sqrt{519845}}{2*1}=\frac{721+\sqrt{519845}}{2}
$