(x^2+8)-6(9+x)=54

Solution for (x^2+8)-6(9+x)=54 equation:

(x^2+8)-6(9+x)=54

We move all terms to the left:

(x^2+8)-6(9+x)-(54)=0

We add all the numbers together, and all the variables

(x^2+8)-6(x+9)-54=0

We multiply parentheses

(x^2+8)-6x-54-54=0

We get rid of parentheses

x^2-6x+8-54-54=0

We add all the numbers together, and all the variables

x^2-6x-100=0

a = 1; b = -6; c = -100;
Δ = b2-4ac
Δ = -62-4·1·(-100)
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{109}}{2*1}=\frac{6-2\sqrt{109}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{109}}{2*1}=\frac{6+2\sqrt{109}}{2}
$