(x)(x+2)=119

Solution for (x)(x+2)=119 equation:

(x)(x+2)=119

We move all terms to the left:

(x)(x+2)-(119)=0

We multiply parentheses

x^2+2x-119=0

a = 1; b = 2; c = -119;
Δ = b2-4ac
Δ = 22-4·1·(-119)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{30}}{2*1}=\frac{-2-4\sqrt{30}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{30}}{2*1}=\frac{-2+4\sqrt{30}}{2}
$