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(2x+5)(x+6)=9
We move all terms to the left:
(2x+5)(x+6)-(9)=0
We multiply parentheses ..
(+2x^2+12x+5x+30)-9=0
We get rid of parentheses
2x^2+12x+5x+30-9=0
We add all the numbers together, and all the variables
2x^2+17x+21=0
a = 2; b = 17; c = +21;
Δ = b2-4ac
Δ = 172-4·2·21
Δ = 121
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{121}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-11}{2*2}=\frac{-28}{4} =-7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+11}{2*2}=\frac{-6}{4} =-1+1/2 $
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