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2/3x-x-8=-10
We move all terms to the left:
2/3x-x-8-(-10)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
-1x+2/3x+2=0
We multiply all the terms by the denominator
-1x*3x+2*3x+2=0
Wy multiply elements
-3x^2+6x+2=0
a = -3; b = 6; c = +2;
Δ = b2-4ac
Δ = 62-4·(-3)·2
Δ = 60
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{15}}{2*-3}=\frac{-6-2\sqrt{15}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{15}}{2*-3}=\frac{-6+2\sqrt{15}}{-6} $
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