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27x(5x+9=19)
We move all terms to the left:
27x(5x+9-(19))=0
We add all the numbers together, and all the variables
27x(5x-10)=0
We multiply parentheses
135x^2-270x=0
a = 135; b = -270; c = 0;
Δ = b2-4ac
Δ = -2702-4·135·0
Δ = 72900
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{72900}=270$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-270}{2*135}=\frac{0}{270} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+270}{2*135}=\frac{540}{270} =2 $
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