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3x(2x-3)=6x+9
We move all terms to the left:
3x(2x-3)-(6x+9)=0
We multiply parentheses
6x^2-9x-(6x+9)=0
We get rid of parentheses
6x^2-9x-6x-9=0
We add all the numbers together, and all the variables
6x^2-15x-9=0
a = 6; b = -15; c = -9;
Δ = b2-4ac
Δ = -152-4·6·(-9)
Δ = 441
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{441}=21$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-21}{2*6}=\frac{-6}{12} =-1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+21}{2*6}=\frac{36}{12} =3 $
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