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-2x(3x+3)+3=5x-9
We move all terms to the left:
-2x(3x+3)+3-(5x-9)=0
We multiply parentheses
-6x^2-6x-(5x-9)+3=0
We get rid of parentheses
-6x^2-6x-5x+9+3=0
We add all the numbers together, and all the variables
-6x^2-11x+12=0
a = -6; b = -11; c = +12;
Δ = b2-4ac
Δ = -112-4·(-6)·12
Δ = 409
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{-(-11)-\sqrt{409}}{2*-6}=\frac{11-\sqrt{409}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{409}}{2*-6}=\frac{11+\sqrt{409}}{-12} $
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