x+2x+3/1x=90

Solution for x+2x+3/1x=90 equation:

x+2x+3/1x=90

We move all terms to the left:

x+2x+3/1x-(90)=0


Domain of the equation: 1x!=0

x∈R


We add all the numbers together, and all the variables

3x+3/1x-90=0

We multiply all the terms by the denominator


3x*1x-90*1x+3=0

Wy multiply elements

3x^2-90x+3=0

a = 3; b = -90; c = +3;
Δ = b2-4ac
Δ = -902-4·3·3
Δ = 8064
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:

$\sqrt{\Delta}=\sqrt{8064}=\sqrt{576*14}=\sqrt{576}*\sqrt{14}=24\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-24\sqrt{14}}{2*3}=\frac{90-24\sqrt{14}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+24\sqrt{14}}{2*3}=\frac{90+24\sqrt{14}}{6}
$