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9x^2+27x=486
We move all terms to the left:
9x^2+27x-(486)=0
a = 9; b = 27; c = -486;
Δ = b2-4ac
Δ = 272-4·9·(-486)
Δ = 18225
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{18225}=135$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-135}{2*9}=\frac{-162}{18} =-9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+135}{2*9}=\frac{108}{18} =6 $
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