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/3x+2x=12-x
We move all terms to the left:
/3x+2x-(12-x)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
/3x+2x-(-1x+12)=0
We add all the numbers together, and all the variables
2x+/3x-(-1x+12)=0
We get rid of parentheses
2x+/3x+1x-12=0
We multiply all the terms by the denominator
2x*3x+1x*3x-12*3x+=0
We add all the numbers together, and all the variables
2x*3x+1x*3x-12*3x=0
Wy multiply elements
6x^2+3x^2-36x=0
We add all the numbers together, and all the variables
9x^2-36x=0
a = 9; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·9·0
Δ = 1296
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{1296}=36$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*9}=\frac{0}{18} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*9}=\frac{72}{18} =4 $
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