1/12x+2x=75

Solution for 1/12x+2x=75 equation:

1/12x+2x=75

We move all terms to the left:

1/12x+2x-(75)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/12x-75=0

We multiply all the terms by the denominator


2x*12x-75*12x+1=0

Wy multiply elements

24x^2-900x+1=0

a = 24; b = -900; c = +1;
Δ = b2-4ac
Δ = -9002-4·24·1
Δ = 809904
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:

$\sqrt{\Delta}=\sqrt{809904}=\sqrt{16*50619}=\sqrt{16}*\sqrt{50619}=4\sqrt{50619}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-900)-4\sqrt{50619}}{2*24}=\frac{900-4\sqrt{50619}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-900)+4\sqrt{50619}}{2*24}=\frac{900+4\sqrt{50619}}{48}
$