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x^2/3+2x-2=0
We multiply all the terms by the denominator
x^2+2x*3-2*3=0
We add all the numbers together, and all the variables
x^2+2x*3-6=0
Wy multiply elements
x^2+6x-6=0
a = 1; b = 6; c = -6;
Δ = b2-4ac
Δ = 62-4·1·(-6)
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*1}=\frac{-6-2\sqrt{15}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{15}}{2*1}=\frac{-6+2\sqrt{15}}{2} $
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