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x(x+8)=12=0

We move all terms to the left:

x(x+8)-(12)=0

We multiply parentheses

x^2+8x-12=0

a = 1; b = 8; c = -12;

Δ = b^{2}-4ac

Δ = 8^{2}-4·1·(-12)

Δ = 112

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{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{7}}{2*1}=\frac{-8-4\sqrt{7}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{7}}{2*1}=\frac{-8+4\sqrt{7}}{2} $

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