-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

-1/3x+7x+18-0=0

We add all the numbers together, and all the variables

7x-1/3x+18=0

We multiply all the terms by the denominator


7x*3x+18*3x-1=0

Wy multiply elements

21x^2+54x-1=0

a = 21; b = 54; c = -1;
Δ = b2-4ac
Δ = 542-4·21·(-1)
Δ = 3000
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:

$\sqrt{\Delta}=\sqrt{3000}=\sqrt{100*30}=\sqrt{100}*\sqrt{30}=10\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-10\sqrt{30}}{2*21}=\frac{-54-10\sqrt{30}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+10\sqrt{30}}{2*21}=\frac{-54+10\sqrt{30}}{42}
$