9(x+23)(x+23)-111=987

Solution for 9(x+23)(x+23)-111=987 equation:

9(x+23)(x+23)-111=987

We move all terms to the left:

9(x+23)(x+23)-111-(987)=0

We add all the numbers together, and all the variables

9(x+23)(x+23)-1098=0

We multiply parentheses ..

9(+x^2+23x+23x+529)-1098=0

We multiply parentheses

9x^2+207x+207x+4761-1098=0

We add all the numbers together, and all the variables

9x^2+414x+3663=0

a = 9; b = 414; c = +3663;
Δ = b2-4ac
Δ = 4142-4·9·3663
Δ = 39528
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{39528}=\sqrt{324*122}=\sqrt{324}*\sqrt{122}=18\sqrt{122}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(414)-18\sqrt{122}}{2*9}=\frac{-414-18\sqrt{122}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(414)+18\sqrt{122}}{2*9}=\frac{-414+18\sqrt{122}}{18}
$