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1/2x+8=1/4x+20
We move all terms to the left:
1/2x+8-(1/4x+20)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 4x+20)!=0We get rid of parentheses
x∈R
1/2x-1/4x-20+8=0
We calculate fractions
4x/8x^2+(-2x)/8x^2-20+8=0
We add all the numbers together, and all the variables
4x/8x^2+(-2x)/8x^2-12=0
We multiply all the terms by the denominator
4x+(-2x)-12*8x^2=0
Wy multiply elements
-96x^2+4x+(-2x)=0
We get rid of parentheses
-96x^2+4x-2x=0
We add all the numbers together, and all the variables
-96x^2+2x=0
a = -96; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-96)·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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-96}=\frac{-4}{-192} =1/48 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-96}=\frac{0}{-192} =0 $
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