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9a-4+3a(a-11)=23
We move all terms to the left:
9a-4+3a(a-11)-(23)=0
We add all the numbers together, and all the variables
9a+3a(a-11)-27=0
We multiply parentheses
3a^2+9a-33a-27=0
We add all the numbers together, and all the variables
3a^2-24a-27=0
a = 3; b = -24; c = -27;
Δ = b2-4ac
Δ = -242-4·3·(-27)
Δ = 900
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{900}=30$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-30}{2*3}=\frac{-6}{6} =-1 $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+30}{2*3}=\frac{54}{6} =9 $
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