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-1/3x-6=x-14
We move all terms to the left:
-1/3x-6-(x-14)=0
Domain of the equation: 3x!=0We get rid of parentheses
x!=0/3
x!=0
x∈R
-1/3x-x+14-6=0
We multiply all the terms by the denominator
-x*3x+14*3x-6*3x-1=0
Wy multiply elements
-3x^2+42x-18x-1=0
We add all the numbers together, and all the variables
-3x^2+24x-1=0
a = -3; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·(-3)·(-1)
Δ = 564
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{564}=\sqrt{4*141}=\sqrt{4}*\sqrt{141}=2\sqrt{141}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{141}}{2*-3}=\frac{-24-2\sqrt{141}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{141}}{2*-3}=\frac{-24+2\sqrt{141}}{-6} $
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