1/2x+1/3x=350

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Solution for 1/2x+1/3x=350 equation:



1/2x+1/3x=350
We move all terms to the left:
1/2x+1/3x-(350)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We calculate fractions
3x/6x^2+2x/6x^2-350=0
We multiply all the terms by the denominator
3x+2x-350*6x^2=0
We add all the numbers together, and all the variables
5x-350*6x^2=0
Wy multiply elements
-2100x^2+5x=0
a = -2100; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-2100)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-2100}=\frac{-10}{-4200} =1/420 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-2100}=\frac{0}{-4200} =0 $

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