4/x+x=225

Solution for 4/x+x=225 equation:

4/x+x=225

We move all terms to the left:

4/x+x-(225)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+4/x-225=0

We multiply all the terms by the denominator


x*x-225*x+4=0

We add all the numbers together, and all the variables

-225x+x*x+4=0

Wy multiply elements

x^2-225x+4=0

a = 1; b = -225; c = +4;
Δ = b2-4ac
Δ = -2252-4·1·4
Δ = 50609
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{-(-225)-\sqrt{50609}}{2*1}=\frac{225-\sqrt{50609}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-225)+\sqrt{50609}}{2*1}=\frac{225+\sqrt{50609}}{2}
$