1/2x-5/6x=10

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Solution for 1/2x-5/6x=10 equation:



1/2x-5/6x=10
We move all terms to the left:
1/2x-5/6x-(10)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
We calculate fractions
6x/12x^2+(-10x)/12x^2-10=0
We multiply all the terms by the denominator
6x+(-10x)-10*12x^2=0
Wy multiply elements
-120x^2+6x+(-10x)=0
We get rid of parentheses
-120x^2+6x-10x=0
We add all the numbers together, and all the variables
-120x^2-4x=0
a = -120; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-120)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-120}=\frac{0}{-240} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-120}=\frac{8}{-240} =-1/30 $

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