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2x(x-5)=x-9
We move all terms to the left:
2x(x-5)-(x-9)=0
We multiply parentheses
2x^2-10x-(x-9)=0
We get rid of parentheses
2x^2-10x-x+9=0
We add all the numbers together, and all the variables
2x^2-11x+9=0
a = 2; b = -11; c = +9;
Δ = b2-4ac
Δ = -112-4·2·9
Δ = 49
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{49}=7$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-7}{2*2}=\frac{4}{4} =1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+7}{2*2}=\frac{18}{4} =4+1/2 $
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