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2/3x+15=17+3/4x
We move all terms to the left:
2/3x+15-(17+3/4x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 4x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
2/3x-(3/4x+17)+15=0
We get rid of parentheses
2/3x-3/4x-17+15=0
We calculate fractions
8x/12x^2+(-9x)/12x^2-17+15=0
We add all the numbers together, and all the variables
8x/12x^2+(-9x)/12x^2-2=0
We multiply all the terms by the denominator
8x+(-9x)-2*12x^2=0
Wy multiply elements
-24x^2+8x+(-9x)=0
We get rid of parentheses
-24x^2+8x-9x=0
We add all the numbers together, and all the variables
-24x^2-1x=0
a = -24; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-24)·0
Δ = 1
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{1}=1$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-24}=\frac{0}{-48} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-24}=\frac{2}{-48} =-1/24 $
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