x(x+2)=7568

Solution for x(x+2)=7568 equation:

x(x+2)=7568

We move all terms to the left:

x(x+2)-(7568)=0

We multiply parentheses

x^2+2x-7568=0

a = 1; b = 2; c = -7568;
Δ = b2-4ac
Δ = 22-4·1·(-7568)
Δ = 30276
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{30276}=174$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-174}{2*1}=\frac{-176}{2}
=-88
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+174}{2*1}=\frac{172}{2}
=86
$