x+22/x+2=30-10

Solution for x+22/x+2=30-10 equation:

x+22/x+2=30-10

We move all terms to the left:

x+22/x+2-(30-10)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+22/x+2-20=0

We add all the numbers together, and all the variables

x+22/x-18=0

We multiply all the terms by the denominator


x*x-18*x+22=0

We add all the numbers together, and all the variables

-18x+x*x+22=0

Wy multiply elements

x^2-18x+22=0

a = 1; b = -18; c = +22;
Δ = b2-4ac
Δ = -182-4·1·22
Δ = 236
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:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{59}}{2*1}=\frac{18-2\sqrt{59}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{59}}{2*1}=\frac{18+2\sqrt{59}}{2}
$