18x+34-6/x=12

Solution for 18x+34-6/x=12 equation:

18x+34-6/x=12

We move all terms to the left:

18x+34-6/x-(12)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

18x-6/x+22=0

We multiply all the terms by the denominator


18x*x+22*x-6=0

We add all the numbers together, and all the variables

22x+18x*x-6=0

Wy multiply elements

18x^2+22x-6=0

a = 18; b = 22; c = -6;
Δ = b2-4ac
Δ = 222-4·18·(-6)
Δ = 916
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:

$\sqrt{\Delta}=\sqrt{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{229}}{2*18}=\frac{-22-2\sqrt{229}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{229}}{2*18}=\frac{-22+2\sqrt{229}}{36}
$