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(6x-9)(9x+9)=0
We multiply parentheses ..
(+54x^2+54x-81x-81)=0
We get rid of parentheses
54x^2+54x-81x-81=0
We add all the numbers together, and all the variables
54x^2-27x-81=0
a = 54; b = -27; c = -81;
Δ = b2-4ac
Δ = -272-4·54·(-81)
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-135}{2*54}=\frac{-108}{108} =-1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+135}{2*54}=\frac{162}{108} =1+1/2 $
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