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84=(x+8)(x)
We move all terms to the left:
84-((x+8)(x))=0
We calculate terms in parentheses: -((x+8)x), so:We get rid of parentheses
(x+8)x
We multiply parentheses
x^2+8x
Back to the equation:
-(x^2+8x)
-x^2-8x+84=0
We add all the numbers together, and all the variables
-1x^2-8x+84=0
a = -1; b = -8; c = +84;
Δ = b2-4ac
Δ = -82-4·(-1)·84
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-20}{2*-1}=\frac{-12}{-2} =+6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+20}{2*-1}=\frac{28}{-2} =-14 $
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