2x*1+x*1+1/2x*2=300

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

2x*1+x*1+1/2x*2=300

We move all terms to the left:

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


Domain of the equation: 2x*2!=0

x!=0/1

x!=0

x∈R


Wy multiply elements

2x+x+1/2x*2-300=0

We multiply all the terms by the denominator


2x*2x*2+x*2x*2-300*2x*2+1=0

Wy multiply elements

8x^2*2+4x^2*2-1200x*2+1=0

Wy multiply elements

16x^2+8x^2-2400x+1=0

We add all the numbers together, and all the variables

24x^2-2400x+1=0

a = 24; b = -2400; c = +1;
Δ = b2-4ac
Δ = -24002-4·24·1
Δ = 5759904
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:

$\sqrt{\Delta}=\sqrt{5759904}=\sqrt{16*359994}=\sqrt{16}*\sqrt{359994}=4\sqrt{359994}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2400)-4\sqrt{359994}}{2*24}=\frac{2400-4\sqrt{359994}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2400)+4\sqrt{359994}}{2*24}=\frac{2400+4\sqrt{359994}}{48}
$