2x+x+1/4x+3=300

Solution for 2x+x+1/4x+3=300 equation:

2x+x+1/4x+3=300

We move all terms to the left:

2x+x+1/4x+3-(300)=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-297=0

We multiply all the terms by the denominator


3x*4x-297*4x+1=0

Wy multiply elements

12x^2-1188x+1=0

a = 12; b = -1188; c = +1;
Δ = b2-4ac
Δ = -11882-4·12·1
Δ = 1411296
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:

$\sqrt{\Delta}=\sqrt{1411296}=\sqrt{16*88206}=\sqrt{16}*\sqrt{88206}=4\sqrt{88206}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1188)-4\sqrt{88206}}{2*12}=\frac{1188-4\sqrt{88206}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1188)+4\sqrt{88206}}{2*12}=\frac{1188+4\sqrt{88206}}{24}
$