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x(x-5)=2x-9
We move all terms to the left:
x(x-5)-(2x-9)=0
We multiply parentheses
x^2-5x-(2x-9)=0
We get rid of parentheses
x^2-5x-2x+9=0
We add all the numbers together, and all the variables
x^2-7x+9=0
a = 1; b = -7; c = +9;
Δ = b2-4ac
Δ = -72-4·1·9
Δ = 13
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{13}}{2*1}=\frac{7-\sqrt{13}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{13}}{2*1}=\frac{7+\sqrt{13}}{2} $
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