(7x+1/12x)=30

Solution for (7x+1/12x)=30 equation:

(7x+1/12x)=30

We move all terms to the left:

(7x+1/12x)-(30)=0


Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+7x+1/12x)-30=0

We get rid of parentheses

7x+1/12x-30=0

We multiply all the terms by the denominator


7x*12x-30*12x+1=0

Wy multiply elements

84x^2-360x+1=0

a = 84; b = -360; c = +1;
Δ = b2-4ac
Δ = -3602-4·84·1
Δ = 129264
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:

$\sqrt{\Delta}=\sqrt{129264}=\sqrt{16*8079}=\sqrt{16}*\sqrt{8079}=4\sqrt{8079}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-4\sqrt{8079}}{2*84}=\frac{360-4\sqrt{8079}}{168}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+4\sqrt{8079}}{2*84}=\frac{360+4\sqrt{8079}}{168}
$