18x=1/228x+18

Solution for 18x=1/228x+18 equation:

18x=1/228x+18

We move all terms to the left:

18x-(1/228x+18)=0


Domain of the equation: 228x+18)!=0

x∈R


We get rid of parentheses

18x-1/228x-18=0

We multiply all the terms by the denominator


18x*228x-18*228x-1=0

Wy multiply elements

4104x^2-4104x-1=0

a = 4104; b = -4104; c = -1;
Δ = b2-4ac
Δ = -41042-4·4104·(-1)
Δ = 16859232
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:

$\sqrt{\Delta}=\sqrt{16859232}=\sqrt{144*117078}=\sqrt{144}*\sqrt{117078}=12\sqrt{117078}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4104)-12\sqrt{117078}}{2*4104}=\frac{4104-12\sqrt{117078}}{8208}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4104)+12\sqrt{117078}}{2*4104}=\frac{4104+12\sqrt{117078}}{8208}
$