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(x-17)x-5=-20
We move all terms to the left:
(x-17)x-5-(-20)=0
We add all the numbers together, and all the variables
(x-17)x+15=0
We multiply parentheses
x^2-17x+15=0
a = 1; b = -17; c = +15;
Δ = b2-4ac
Δ = -172-4·1·15
Δ = 229
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{-(-17)-\sqrt{229}}{2*1}=\frac{17-\sqrt{229}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{229}}{2*1}=\frac{17+\sqrt{229}}{2} $
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