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6x^2+9x-12=2
We move all terms to the left:
6x^2+9x-12-(2)=0
We add all the numbers together, and all the variables
6x^2+9x-14=0
a = 6; b = 9; c = -14;
Δ = b2-4ac
Δ = 92-4·6·(-14)
Δ = 417
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{-(9)-\sqrt{417}}{2*6}=\frac{-9-\sqrt{417}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{417}}{2*6}=\frac{-9+\sqrt{417}}{12} $
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