x(2x+12)=244

Solution for x(2x+12)=244 equation:

x(2x+12)=244

We move all terms to the left:

x(2x+12)-(244)=0

We multiply parentheses

2x^2+12x-244=0

a = 2; b = 12; c = -244;
Δ = b2-4ac
Δ = 122-4·2·(-244)
Δ = 2096
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:

$\sqrt{\Delta}=\sqrt{2096}=\sqrt{16*131}=\sqrt{16}*\sqrt{131}=4\sqrt{131}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{131}}{2*2}=\frac{-12-4\sqrt{131}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{131}}{2*2}=\frac{-12+4\sqrt{131}}{4}
$