X(2x+12)=260

Solution for X(2x+12)=260 equation:

X(2X+12)=260

We move all terms to the left:

X(2X+12)-(260)=0

We multiply parentheses

2X^2+12X-260=0

a = 2; b = 12; c = -260;
Δ = b2-4ac
Δ = 122-4·2·(-260)
Δ = 2224
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:

$\sqrt{\Delta}=\sqrt{2224}=\sqrt{16*139}=\sqrt{16}*\sqrt{139}=4\sqrt{139}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{139}}{2*2}=\frac{-12-4\sqrt{139}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{139}}{2*2}=\frac{-12+4\sqrt{139}}{4}
$