1/4x+3x=180

Solution for 1/4x+3x=180 equation:

1/4x+3x=180

We move all terms to the left:

1/4x+3x-(180)=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-180=0

We multiply all the terms by the denominator


3x*4x-180*4x+1=0

Wy multiply elements

12x^2-720x+1=0

a = 12; b = -720; c = +1;
Δ = b2-4ac
Δ = -7202-4·12·1
Δ = 518352
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:

$\sqrt{\Delta}=\sqrt{518352}=\sqrt{16*32397}=\sqrt{16}*\sqrt{32397}=4\sqrt{32397}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-720)-4\sqrt{32397}}{2*12}=\frac{720-4\sqrt{32397}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-720)+4\sqrt{32397}}{2*12}=\frac{720+4\sqrt{32397}}{24}
$