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-1/2x+8=1/4x+16
We move all terms to the left:
-1/2x+8-(1/4x+16)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 4x+16)!=0We get rid of parentheses
x∈R
-1/2x-1/4x-16+8=0
We calculate fractions
(-4x)/8x^2+(-2x)/8x^2-16+8=0
We add all the numbers together, and all the variables
(-4x)/8x^2+(-2x)/8x^2-8=0
We multiply all the terms by the denominator
(-4x)+(-2x)-8*8x^2=0
Wy multiply elements
-64x^2+(-4x)+(-2x)=0
We get rid of parentheses
-64x^2-4x-2x=0
We add all the numbers together, and all the variables
-64x^2-6x=0
a = -64; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-64)·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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-64}=\frac{0}{-128} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-64}=\frac{12}{-128} =-3/32 $
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