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4a+8=a(a+2)
We move all terms to the left:
4a+8-(a(a+2))=0
We calculate terms in parentheses: -(a(a+2)), so:We get rid of parentheses
a(a+2)
We multiply parentheses
a^2+2a
Back to the equation:
-(a^2+2a)
-a^2+4a-2a+8=0
We add all the numbers together, and all the variables
-1a^2+2a+8=0
a = -1; b = 2; c = +8;
Δ = b2-4ac
Δ = 22-4·(-1)·8
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{36}=6$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6}{2*-1}=\frac{-8}{-2} =+4 $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6}{2*-1}=\frac{4}{-2} =-2 $
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