x(2x+6)+6^2=116

Solution for x(2x+6)+6^2=116 equation:

x(2x+6)+6^2=116

We move all terms to the left:

x(2x+6)+6^2-(116)=0

determiningTheFunctionDomain
x(2x+6)-116+6^2=0

We add all the numbers together, and all the variables

x(2x+6)-80=0

We multiply parentheses

2x^2+6x-80=0

a = 2; b = 6; c = -80;
Δ = b2-4ac
Δ = 62-4·2·(-80)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-26}{2*2}=\frac{-32}{4}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+26}{2*2}=\frac{20}{4}
=5
$