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3x-x^2=-54
We move all terms to the left:
3x-x^2-(-54)=0
We add all the numbers together, and all the variables
-1x^2+3x+54=0
a = -1; b = 3; c = +54;
Δ = b2-4ac
Δ = 32-4·(-1)·54
Δ = 225
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{225}=15$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-15}{2*-1}=\frac{-18}{-2} =+9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+15}{2*-1}=\frac{12}{-2} =-6 $
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