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(a-7)(a+6)=-2a
We move all terms to the left:
(a-7)(a+6)-(-2a)=0
We get rid of parentheses
(a-7)(a+6)+2a=0
We multiply parentheses ..
(+a^2+6a-7a-42)+2a=0
We get rid of parentheses
a^2+6a-7a+2a-42=0
We add all the numbers together, and all the variables
a^2+a-42=0
a = 1; b = 1; c = -42;
Δ = b2-4ac
Δ = 12-4·1·(-42)
Δ = 169
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{169}=13$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-13}{2*1}=\frac{-14}{2} =-7 $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+13}{2*1}=\frac{12}{2} =6 $
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