1/3x+7x+18=84

Solution for 1/3x+7x+18=84 equation:

1/3x+7x+18=84

We move all terms to the left:

1/3x+7x+18-(84)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

7x+1/3x-66=0

We multiply all the terms by the denominator


7x*3x-66*3x+1=0

Wy multiply elements

21x^2-198x+1=0

a = 21; b = -198; c = +1;
Δ = b2-4ac
Δ = -1982-4·21·1
Δ = 39120
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:

$\sqrt{\Delta}=\sqrt{39120}=\sqrt{16*2445}=\sqrt{16}*\sqrt{2445}=4\sqrt{2445}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-198)-4\sqrt{2445}}{2*21}=\frac{198-4\sqrt{2445}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-198)+4\sqrt{2445}}{2*21}=\frac{198+4\sqrt{2445}}{42}
$