(x)(x+1)(2)=182

Solution for (x)(x+1)(2)=182 equation:

(x)(x+1)(2)=182

We move all terms to the left:

(x)(x+1)(2)-(182)=0

We multiply parentheses

2x^2+2x-182=0

a = 2; b = 2; c = -182;
Δ = b2-4ac
Δ = 22-4·2·(-182)
Δ = 1460
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:

$\sqrt{\Delta}=\sqrt{1460}=\sqrt{4*365}=\sqrt{4}*\sqrt{365}=2\sqrt{365}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{365}}{2*2}=\frac{-2-2\sqrt{365}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{365}}{2*2}=\frac{-2+2\sqrt{365}}{4}
$