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2/3x+.132x+6=x
We move all terms to the left:
2/3x+.132x+6-(x)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
-0.868x+2/3x+6=0
We multiply all the terms by the denominator
-(0.868x)*3x+6*3x+2=0
We add all the numbers together, and all the variables
-(+0.868x)*3x+6*3x+2=0
We multiply parentheses
-0x^2+6*3x+2=0
Wy multiply elements
-0x^2+18x+2=0
We add all the numbers together, and all the variables
-1x^2+18x+2=0
a = -1; b = 18; c = +2;
Δ = b2-4ac
Δ = 182-4·(-1)·2
Δ = 332
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{332}=\sqrt{4*83}=\sqrt{4}*\sqrt{83}=2\sqrt{83}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{83}}{2*-1}=\frac{-18-2\sqrt{83}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{83}}{2*-1}=\frac{-18+2\sqrt{83}}{-2} $
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