9a-4+3a(a-11)=23

Solution for 9a-4+3a(a-11)=23 equation:

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
$