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5/8x+8=1/4x=5x
We move all terms to the left:
5/8x+8-(1/4x)=0
Domain of the equation: 8x!=0
x!=0/8
x!=0
x∈R
Domain of the equation: 4x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
5/8x-(+1/4x)+8=0
We get rid of parentheses
5/8x-1/4x+8=0
We calculate fractions
20x/32x^2+(-8x)/32x^2+8=0
We multiply all the terms by the denominator
20x+(-8x)+8*32x^2=0
Wy multiply elements
256x^2+20x+(-8x)=0
We get rid of parentheses
256x^2+20x-8x=0
We add all the numbers together, and all the variables
256x^2+12x=0
a = 256; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·256·0
Δ = 144
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{144}=12$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*256}=\frac{-24}{512} =-3/64 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*256}=\frac{0}{512} =0 $
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