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23-(a+11)a=7
We move all terms to the left:
23-(a+11)a-(7)=0
We add all the numbers together, and all the variables
-(a+11)a+16=0
We multiply parentheses
-a^2-11a+16=0
We add all the numbers together, and all the variables
-1a^2-11a+16=0
a = -1; b = -11; c = +16;
Δ = b2-4ac
Δ = -112-4·(-1)·16
Δ = 185
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}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{185}}{2*-1}=\frac{11-\sqrt{185}}{-2} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{185}}{2*-1}=\frac{11+\sqrt{185}}{-2} $
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