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X=-3X^2+12X+9
We move all terms to the left:
X-(-3X^2+12X+9)=0
We get rid of parentheses
3X^2-12X+X-9=0
We add all the numbers together, and all the variables
3X^2-11X-9=0
a = 3; b = -11; c = -9;
Δ = b2-4ac
Δ = -112-4·3·(-9)
Δ = 229
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{229}}{2*3}=\frac{11-\sqrt{229}}{6} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{229}}{2*3}=\frac{11+\sqrt{229}}{6} $
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