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1/2x+3=5/8x-1
We move all terms to the left:
1/2x+3-(5/8x-1)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 8x-1)!=0We get rid of parentheses
x∈R
1/2x-5/8x+1+3=0
We calculate fractions
8x/16x^2+(-10x)/16x^2+1+3=0
We add all the numbers together, and all the variables
8x/16x^2+(-10x)/16x^2+4=0
We multiply all the terms by the denominator
8x+(-10x)+4*16x^2=0
Wy multiply elements
64x^2+8x+(-10x)=0
We get rid of parentheses
64x^2+8x-10x=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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*64}=\frac{0}{128} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*64}=\frac{4}{128} =1/32 $
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