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3/4x+16=1/8x+2
We move all terms to the left:
3/4x+16-(1/8x+2)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 8x+2)!=0We get rid of parentheses
x∈R
3/4x-1/8x-2+16=0
We calculate fractions
24x/32x^2+(-4x)/32x^2-2+16=0
We add all the numbers together, and all the variables
24x/32x^2+(-4x)/32x^2+14=0
We multiply all the terms by the denominator
24x+(-4x)+14*32x^2=0
Wy multiply elements
448x^2+24x+(-4x)=0
We get rid of parentheses
448x^2+24x-4x=0
We add all the numbers together, and all the variables
448x^2+20x=0
a = 448; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·448·0
Δ = 400
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{400}=20$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*448}=\frac{-40}{896} =-5/112 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*448}=\frac{0}{896} =0 $
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