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x2+8x+19=8
We move all terms to the left:
x2+8x+19-(8)=0
We add all the numbers together, and all the variables
x^2+8x+11=0
a = 1; b = 8; c = +11;
Δ = b2-4ac
Δ = 82-4·1·11
Δ = 20
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{5}}{2*1}=\frac{-8-2\sqrt{5}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{5}}{2*1}=\frac{-8+2\sqrt{5}}{2} $
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