1/2x+3x-2750=0

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Solution for 1/2x+3x-2750=0 equation: 



1/2x+3x-2750=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-2750=0

We multiply all the terms by the denominator


3x*2x-2750*2x+1=0

Wy multiply elements

6x^2-5500x+1=0

a = 6; b = -5500; c = +1;
Δ = b2-4ac
Δ = -55002-4·6·1
Δ = 30249976
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:


$\sqrt{\Delta}=\sqrt{30249976}=\sqrt{4*7562494}=\sqrt{4}*\sqrt{7562494}=2\sqrt{7562494}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5500)-2\sqrt{7562494}}{2*6}=\frac{5500-2\sqrt{7562494}}{12}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5500)+2\sqrt{7562494}}{2*6}=\frac{5500+2\sqrt{7562494}}{12}
$

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