3x+12/x=22

Solution for 3x+12/x=22 equation:

3x+12/x=22

We move all terms to the left:

3x+12/x-(22)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


3x*x-22*x+12=0

We add all the numbers together, and all the variables

-22x+3x*x+12=0

Wy multiply elements

3x^2-22x+12=0

a = 3; b = -22; c = +12;
Δ = b2-4ac
Δ = -222-4·3·12
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{85}}{2*3}=\frac{22-2\sqrt{85}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{85}}{2*3}=\frac{22+2\sqrt{85}}{6}
$