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-2/3x+20=-1/4x+12
We move all terms to the left:
-2/3x+20-(-1/4x+12)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 4x+12)!=0We get rid of parentheses
x∈R
-2/3x+1/4x-12+20=0
We calculate fractions
(-8x)/12x^2+3x/12x^2-12+20=0
We add all the numbers together, and all the variables
(-8x)/12x^2+3x/12x^2+8=0
We multiply all the terms by the denominator
(-8x)+3x+8*12x^2=0
We add all the numbers together, and all the variables
3x+(-8x)+8*12x^2=0
Wy multiply elements
96x^2+3x+(-8x)=0
We get rid of parentheses
96x^2+3x-8x=0
We add all the numbers together, and all the variables
96x^2-5x=0
a = 96; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·96·0
Δ = 25
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{25}=5$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*96}=\frac{0}{192} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*96}=\frac{10}{192} =5/96 $
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