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1/2x+2=3/8x-2
We move all terms to the left:
1/2x+2-(3/8x-2)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 8x-2)!=0We get rid of parentheses
x∈R
1/2x-3/8x+2+2=0
We calculate fractions
8x/16x^2+(-6x)/16x^2+2+2=0
We add all the numbers together, and all the variables
8x/16x^2+(-6x)/16x^2+4=0
We multiply all the terms by the denominator
8x+(-6x)+4*16x^2=0
Wy multiply elements
64x^2+8x+(-6x)=0
We get rid of parentheses
64x^2+8x-6x=0
We add all the numbers together, and all the variables
64x^2+2x=0
a = 64; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·64·0
Δ = 4
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{4}=2$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*64}=\frac{-4}{128} =-1/32 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*64}=\frac{0}{128} =0 $
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