2/x+(x+22)+x=232

Solution for 2/x+(x+22)+x=232 equation:

2/x+(x+22)+x=232

We move all terms to the left:

2/x+(x+22)+x-(232)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+2/x+(x+22)-232=0

We get rid of parentheses

x+2/x+x+22-232=0

We multiply all the terms by the denominator


x*x+x*x+22*x-232*x+2=0

We add all the numbers together, and all the variables

-210x+x*x+x*x+2=0

Wy multiply elements

x^2+x^2-210x+2=0

We add all the numbers together, and all the variables

2x^2-210x+2=0

a = 2; b = -210; c = +2;
Δ = b2-4ac
Δ = -2102-4·2·2
Δ = 44084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{44084}=\sqrt{4*11021}=\sqrt{4}*\sqrt{11021}=2\sqrt{11021}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-2\sqrt{11021}}{2*2}=\frac{210-2\sqrt{11021}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+2\sqrt{11021}}{2*2}=\frac{210+2\sqrt{11021}}{4}
$