(26.25/x)+3=x

Solution for (26.25/x)+3=x equation:

(26.25/x)+3=x

We move all terms to the left:

(26.25/x)+3-(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

(+26.25/x)-x+3=0

We add all the numbers together, and all the variables

-1x+(+26.25/x)+3=0

We get rid of parentheses

-1x+26.25/x+3=0

We multiply all the terms by the denominator


-1x*x+3*x+26.25=0

We add all the numbers together, and all the variables

3x-1x*x+26.25=0

Wy multiply elements

-1x^2+3x+26.25=0

a = -1; b = 3; c = +26.25;
Δ = b2-4ac
Δ = 32-4·(-1)·26.25
Δ = 114
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{-(3)-\sqrt{114}}{2*-1}=\frac{-3-\sqrt{114}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{114}}{2*-1}=\frac{-3+\sqrt{114}}{-2}
$