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5/8x+4=3/6x+12
We move all terms to the left:
5/8x+4-(3/6x+12)=0
Domain of the equation: 8x!=0
x!=0/8
x!=0
x∈R
Domain of the equation: 6x+12)!=0We get rid of parentheses
x∈R
5/8x-3/6x-12+4=0
We calculate fractions
30x/48x^2+(-24x)/48x^2-12+4=0
We add all the numbers together, and all the variables
30x/48x^2+(-24x)/48x^2-8=0
We multiply all the terms by the denominator
30x+(-24x)-8*48x^2=0
Wy multiply elements
-384x^2+30x+(-24x)=0
We get rid of parentheses
-384x^2+30x-24x=0
We add all the numbers together, and all the variables
-384x^2+6x=0
a = -384; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-384)·0
Δ = 36
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{36}=6$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-384}=\frac{-12}{-768} =1/64 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-384}=\frac{0}{-768} =0 $
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