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17=x2+5x+8
We move all terms to the left:
17-(x2+5x+8)=0
We add all the numbers together, and all the variables
-(+x^2+5x+8)+17=0
We get rid of parentheses
-x^2-5x-8+17=0
We add all the numbers together, and all the variables
-1x^2-5x+9=0
a = -1; b = -5; c = +9;
Δ = b2-4ac
Δ = -52-4·(-1)·9
Δ = 61
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{61}}{2*-1}=\frac{5-\sqrt{61}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{61}}{2*-1}=\frac{5+\sqrt{61}}{-2} $
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