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3/4x+1/2x+5/6=3/9
We move all terms to the left:
3/4x+1/2x+5/6-(3/9)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
3/4x+1/2x+5/6-(+3/9)=0
We get rid of parentheses
3/4x+1/2x+5/6-3/9=0
We calculate fractions
(-288x^2)/2592x^2+720x^2/2592x^2+1944x/2592x^2+1296x/2592x^2=0
We multiply all the terms by the denominator
(-288x^2)+720x^2+1944x+1296x=0
We add all the numbers together, and all the variables
720x^2+(-288x^2)+3240x=0
We get rid of parentheses
720x^2-288x^2+3240x=0
We add all the numbers together, and all the variables
432x^2+3240x=0
a = 432; b = 3240; c = 0;
Δ = b2-4ac
Δ = 32402-4·432·0
Δ = 10497600
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{10497600}=3240$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3240)-3240}{2*432}=\frac{-6480}{864} =-7+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3240)+3240}{2*432}=\frac{0}{864} =0 $
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