x(x+8)=-13

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Solution for x(x+8)=-13 equation:



x(x+8)=-13
We move all terms to the left:
x(x+8)-(-13)=0
We add all the numbers together, and all the variables
x(x+8)+13=0
We multiply parentheses
x^2+8x+13=0
a = 1; b = 8; c = +13;
Δ = b2-4ac
Δ = 82-4·1·13
Δ = 12
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:
$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{3}}{2*1}=\frac{-8-2\sqrt{3}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{3}}{2*1}=\frac{-8+2\sqrt{3}}{2} $

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