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(6x-19)(9x+11)=0
We multiply parentheses ..
(+54x^2+66x-171x-209)=0
We get rid of parentheses
54x^2+66x-171x-209=0
We add all the numbers together, and all the variables
54x^2-105x-209=0
a = 54; b = -105; c = -209;
Δ = b2-4ac
Δ = -1052-4·54·(-209)
Δ = 56169
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{56169}=237$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-237}{2*54}=\frac{-132}{108} =-1+2/9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+237}{2*54}=\frac{342}{108} =3+1/6 $
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