(x+3)(x+3)=567

Solution for (x+3)(x+3)=567 equation:

(x+3)(x+3)=567

We move all terms to the left:

(x+3)(x+3)-(567)=0

We multiply parentheses ..

(+x^2+3x+3x+9)-567=0

We get rid of parentheses

x^2+3x+3x+9-567=0

We add all the numbers together, and all the variables

x^2+6x-558=0

a = 1; b = 6; c = -558;
Δ = b2-4ac
Δ = 62-4·1·(-558)
Δ = 2268
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:

$\sqrt{\Delta}=\sqrt{2268}=\sqrt{324*7}=\sqrt{324}*\sqrt{7}=18\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-18\sqrt{7}}{2*1}=\frac{-6-18\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+18\sqrt{7}}{2*1}=\frac{-6+18\sqrt{7}}{2}
$