1/4x+2x+12=39

Solution for 1/4x+2x+12=39 equation:

1/4x+2x+12=39

We move all terms to the left:

1/4x+2x+12-(39)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/4x-27=0

We multiply all the terms by the denominator


2x*4x-27*4x+1=0

Wy multiply elements

8x^2-108x+1=0

a = 8; b = -108; c = +1;
Δ = b2-4ac
Δ = -1082-4·8·1
Δ = 11632
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:

$\sqrt{\Delta}=\sqrt{11632}=\sqrt{16*727}=\sqrt{16}*\sqrt{727}=4\sqrt{727}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-4\sqrt{727}}{2*8}=\frac{108-4\sqrt{727}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+4\sqrt{727}}{2*8}=\frac{108+4\sqrt{727}}{16}
$