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x^2+6x-2x-12=9
We move all terms to the left:
x^2+6x-2x-12-(9)=0
We add all the numbers together, and all the variables
x^2+4x-21=0
a = 1; b = 4; c = -21;
Δ = b2-4ac
Δ = 42-4·1·(-21)
Δ = 100
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{100}=10$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-10}{2*1}=\frac{-14}{2} =-7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+10}{2*1}=\frac{6}{2} =3 $
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