x(2x+12)=182

Solution for x(2x+12)=182 equation:

x(2x+12)=182

We move all terms to the left:

x(2x+12)-(182)=0

We multiply parentheses

2x^2+12x-182=0

a = 2; b = 12; c = -182;
Δ = b2-4ac
Δ = 122-4·2·(-182)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-40}{2*2}=\frac{-52}{4}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+40}{2*2}=\frac{28}{4}
=7
$