1/4x+3x=72

Solution for 1/4x+3x=72 equation:

1/4x+3x=72

We move all terms to the left:

1/4x+3x-(72)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/4x-72=0

We multiply all the terms by the denominator


3x*4x-72*4x+1=0

Wy multiply elements

12x^2-288x+1=0

a = 12; b = -288; c = +1;
Δ = b2-4ac
Δ = -2882-4·12·1
Δ = 82896
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:

$\sqrt{\Delta}=\sqrt{82896}=\sqrt{16*5181}=\sqrt{16}*\sqrt{5181}=4\sqrt{5181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-288)-4\sqrt{5181}}{2*12}=\frac{288-4\sqrt{5181}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-288)+4\sqrt{5181}}{2*12}=\frac{288+4\sqrt{5181}}{24}
$