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-17+5x(x-1)=2x-9
We move all terms to the left:
-17+5x(x-1)-(2x-9)=0
We multiply parentheses
5x^2-5x-(2x-9)-17=0
We get rid of parentheses
5x^2-5x-2x+9-17=0
We add all the numbers together, and all the variables
5x^2-7x-8=0
a = 5; b = -7; c = -8;
Δ = b2-4ac
Δ = -72-4·5·(-8)
Δ = 209
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{-(-7)-\sqrt{209}}{2*5}=\frac{7-\sqrt{209}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{209}}{2*5}=\frac{7+\sqrt{209}}{10} $
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