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9x(x+3)=27
We move all terms to the left:
9x(x+3)-(27)=0
We multiply parentheses
9x^2+27x-27=0
a = 9; b = 27; c = -27;
Δ = b2-4ac
Δ = 272-4·9·(-27)
Δ = 1701
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1701}=\sqrt{81*21}=\sqrt{81}*\sqrt{21}=9\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-9\sqrt{21}}{2*9}=\frac{-27-9\sqrt{21}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+9\sqrt{21}}{2*9}=\frac{-27+9\sqrt{21}}{18} $
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