x(2x+6)=126

Solution for x(2x+6)=126 equation:

x(2x+6)=126

We move all terms to the left:

x(2x+6)-(126)=0

We multiply parentheses

2x^2+6x-126=0

a = 2; b = 6; c = -126;
Δ = b2-4ac
Δ = 62-4·2·(-126)
Δ = 1044
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:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{29}}{2*2}=\frac{-6-6\sqrt{29}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{29}}{2*2}=\frac{-6+6\sqrt{29}}{4}
$