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2/3x+x=10-3
We move all terms to the left:
2/3x+x-(10-3)=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+x-7=0
We add all the numbers together, and all the variables
x+2/3x-7=0
We multiply all the terms by the denominator
x*3x-7*3x+2=0
Wy multiply elements
3x^2-21x+2=0
a = 3; b = -21; c = +2;
Δ = b2-4ac
Δ = -212-4·3·2
Δ = 417
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{-(-21)-\sqrt{417}}{2*3}=\frac{21-\sqrt{417}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{417}}{2*3}=\frac{21+\sqrt{417}}{6} $
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