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20=2a+a^2
We move all terms to the left:
20-(2a+a^2)=0
We get rid of parentheses
-a^2-2a+20=0
We add all the numbers together, and all the variables
-1a^2-2a+20=0
a = -1; b = -2; c = +20;
Δ = b2-4ac
Δ = -22-4·(-1)·20
Δ = 84
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}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{21}}{2*-1}=\frac{2-2\sqrt{21}}{-2} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{21}}{2*-1}=\frac{2+2\sqrt{21}}{-2} $
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