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(5x+2)(x-3)=9
We move all terms to the left:
(5x+2)(x-3)-(9)=0
We multiply parentheses ..
(+5x^2-15x+2x-6)-9=0
We get rid of parentheses
5x^2-15x+2x-6-9=0
We add all the numbers together, and all the variables
5x^2-13x-15=0
a = 5; b = -13; c = -15;
Δ = b2-4ac
Δ = -132-4·5·(-15)
Δ = 469
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{-(-13)-\sqrt{469}}{2*5}=\frac{13-\sqrt{469}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{469}}{2*5}=\frac{13+\sqrt{469}}{10} $
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