(x+3)(x+3)-5=84

Solution for (x+3)(x+3)-5=84 equation:

(x+3)(x+3)-5=84

We move all terms to the left:

(x+3)(x+3)-5-(84)=0

We add all the numbers together, and all the variables

(x+3)(x+3)-89=0

We multiply parentheses ..

(+x^2+3x+3x+9)-89=0

We get rid of parentheses

x^2+3x+3x+9-89=0

We add all the numbers together, and all the variables

x^2+6x-80=0

a = 1; b = 6; c = -80;
Δ = b2-4ac
Δ = 62-4·1·(-80)
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{89}}{2*1}=\frac{-6-2\sqrt{89}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{89}}{2*1}=\frac{-6+2\sqrt{89}}{2}
$