x(x+2)=84

Solution for x(x+2)=84 equation:

x(x+2)=84

We move all terms to the left:

x(x+2)-(84)=0

We multiply parentheses

x^2+2x-84=0

a = 1; b = 2; c = -84;
Δ = b2-4ac
Δ = 22-4·1·(-84)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{85}}{2*1}=\frac{-2-2\sqrt{85}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{85}}{2*1}=\frac{-2+2\sqrt{85}}{2}
$