X=14.50+17.25/x

Solution for X=14.50+17.25/x equation:

X=14.50+17.25/X

We move all terms to the left:

X-(14.50+17.25/X)=0


Domain of the equation: X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(17.25/X+14.5)=0

We get rid of parentheses

X-17.25/X-14.5=0

We multiply all the terms by the denominator


X*X-(14.5)*X-17.25=0

We multiply parentheses

X*X-14.5X-17.25=0

Wy multiply elements

X^2-14.5X-17.25=0

a = 1; b = -14.5; c = -17.25;
Δ = b2-4ac
Δ = -14.52-4·1·(-17.25)
Δ = 279.25
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{-(-14.5)-\sqrt{279.25}}{2*1}=\frac{14.5-\sqrt{279.25}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14.5)+\sqrt{279.25}}{2*1}=\frac{14.5+\sqrt{279.25}}{2}
$