x+2/x+12=90

Solution for x+2/x+12=90 equation:

x+2/x+12=90

We move all terms to the left:

x+2/x+12-(90)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+2/x-78=0

We multiply all the terms by the denominator


x*x-78*x+2=0

We add all the numbers together, and all the variables

-78x+x*x+2=0

Wy multiply elements

x^2-78x+2=0

a = 1; b = -78; c = +2;
Δ = b2-4ac
Δ = -782-4·1·2
Δ = 6076
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:

$\sqrt{\Delta}=\sqrt{6076}=\sqrt{196*31}=\sqrt{196}*\sqrt{31}=14\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-14\sqrt{31}}{2*1}=\frac{78-14\sqrt{31}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+14\sqrt{31}}{2*1}=\frac{78+14\sqrt{31}}{2}
$