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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/2x-297=0

We multiply all the terms by the denominator


3x*2x-297*2x+1=0

Wy multiply elements

6x^2-594x+1=0

a = 6; b = -594; c = +1;
Δ = b2-4ac
Δ = -5942-4·6·1
Δ = 352812
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:

$\sqrt{\Delta}=\sqrt{352812}=\sqrt{4*88203}=\sqrt{4}*\sqrt{88203}=2\sqrt{88203}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-594)-2\sqrt{88203}}{2*6}=\frac{594-2\sqrt{88203}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-594)+2\sqrt{88203}}{2*6}=\frac{594+2\sqrt{88203}}{12}
$