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2/3x+4=1/4x-9
We move all terms to the left:
2/3x+4-(1/4x-9)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 4x-9)!=0We get rid of parentheses
x∈R
2/3x-1/4x+9+4=0
We calculate fractions
8x/12x^2+(-3x)/12x^2+9+4=0
We add all the numbers together, and all the variables
8x/12x^2+(-3x)/12x^2+13=0
We multiply all the terms by the denominator
8x+(-3x)+13*12x^2=0
Wy multiply elements
156x^2+8x+(-3x)=0
We get rid of parentheses
156x^2+8x-3x=0
We add all the numbers together, and all the variables
156x^2+5x=0
a = 156; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·156·0
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*156}=\frac{-10}{312} =-5/156 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*156}=\frac{0}{312} =0 $
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