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5x(x+4)=x-9
We move all terms to the left:
5x(x+4)-(x-9)=0
We multiply parentheses
5x^2+20x-(x-9)=0
We get rid of parentheses
5x^2+20x-x+9=0
We add all the numbers together, and all the variables
5x^2+19x+9=0
a = 5; b = 19; c = +9;
Δ = b2-4ac
Δ = 192-4·5·9
Δ = 181
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{-(19)-\sqrt{181}}{2*5}=\frac{-19-\sqrt{181}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{181}}{2*5}=\frac{-19+\sqrt{181}}{10} $
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