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x^2+6x-82=9
We move all terms to the left:
x^2+6x-82-(9)=0
We add all the numbers together, and all the variables
x^2+6x-91=0
a = 1; b = 6; c = -91;
Δ = b2-4ac
Δ = 62-4·1·(-91)
Δ = 400
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{400}=20$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-20}{2*1}=\frac{-26}{2} =-13 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+20}{2*1}=\frac{14}{2} =7 $
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