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6x^2+5x-27=-6
We move all terms to the left:
6x^2+5x-27-(-6)=0
We add all the numbers together, and all the variables
6x^2+5x-21=0
a = 6; b = 5; c = -21;
Δ = b2-4ac
Δ = 52-4·6·(-21)
Δ = 529
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{529}=23$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-23}{2*6}=\frac{-28}{12} =-2+1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+23}{2*6}=\frac{18}{12} =1+1/2 $
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