(x+7)(x+7)=216

Solution for (x+7)(x+7)=216 equation:

(x+7)(x+7)=216

We move all terms to the left:

(x+7)(x+7)-(216)=0

We multiply parentheses ..

(+x^2+7x+7x+49)-216=0

We get rid of parentheses

x^2+7x+7x+49-216=0

We add all the numbers together, and all the variables

x^2+14x-167=0

a = 1; b = 14; c = -167;
Δ = b2-4ac
Δ = 142-4·1·(-167)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-12\sqrt{6}}{2*1}=\frac{-14-12\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+12\sqrt{6}}{2*1}=\frac{-14+12\sqrt{6}}{2}
$