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5x^2+20x+19=8
We move all terms to the left:
5x^2+20x+19-(8)=0
We add all the numbers together, and all the variables
5x^2+20x+11=0
a = 5; b = 20; c = +11;
Δ = b2-4ac
Δ = 202-4·5·11
Δ = 180
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-6\sqrt{5}}{2*5}=\frac{-20-6\sqrt{5}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+6\sqrt{5}}{2*5}=\frac{-20+6\sqrt{5}}{10} $
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