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-1-2/3x+8=4-x
We move all terms to the left:
-1-2/3x+8-(4-x)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
-2/3x-(-1x+4)-1+8=0
We add all the numbers together, and all the variables
-2/3x-(-1x+4)+7=0
We get rid of parentheses
-2/3x+1x-4+7=0
We multiply all the terms by the denominator
1x*3x-4*3x+7*3x-2=0
Wy multiply elements
3x^2-12x+21x-2=0
We add all the numbers together, and all the variables
3x^2+9x-2=0
a = 3; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·3·(-2)
Δ = 105
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{105}}{2*3}=\frac{-9-\sqrt{105}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{105}}{2*3}=\frac{-9+\sqrt{105}}{6} $
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