1/2x+2/3x=5

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Solution for 1/2x+2/3x=5 equation:



1/2x+2/3x=5
We move all terms to the left:
1/2x+2/3x-(5)=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+4x/6x^2-5=0
We multiply all the terms by the denominator
3x+4x-5*6x^2=0
We add all the numbers together, and all the variables
7x-5*6x^2=0
Wy multiply elements
-30x^2+7x=0
a = -30; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-30)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-30}=\frac{-14}{-60} =7/30 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-30}=\frac{0}{-60} =0 $

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