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(5x-1)(x-17)=x
We move all terms to the left:
(5x-1)(x-17)-(x)=0
We add all the numbers together, and all the variables
-1x+(5x-1)(x-17)=0
We multiply parentheses ..
(+5x^2-85x-1x+17)-1x=0
We get rid of parentheses
5x^2-85x-1x-1x+17=0
We add all the numbers together, and all the variables
5x^2-87x+17=0
a = 5; b = -87; c = +17;
Δ = b2-4ac
Δ = -872-4·5·17
Δ = 7229
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{-(-87)-\sqrt{7229}}{2*5}=\frac{87-\sqrt{7229}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-87)+\sqrt{7229}}{2*5}=\frac{87+\sqrt{7229}}{10} $
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