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6x^2+x-2=8
We move all terms to the left:
6x^2+x-2-(8)=0
We add all the numbers together, and all the variables
6x^2+x-10=0
a = 6; b = 1; c = -10;
Δ = b2-4ac
Δ = 12-4·6·(-10)
Δ = 241
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{-(1)-\sqrt{241}}{2*6}=\frac{-1-\sqrt{241}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{241}}{2*6}=\frac{-1+\sqrt{241}}{12} $
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