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6(x-9)(4x+1)=0
We multiply parentheses ..
6(+4x^2+x-36x-9)=0
We multiply parentheses
24x^2+6x-216x-54=0
We add all the numbers together, and all the variables
24x^2-210x-54=0
a = 24; b = -210; c = -54;
Δ = b2-4ac
Δ = -2102-4·24·(-54)
Δ = 49284
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{49284}=222$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-222}{2*24}=\frac{-12}{48} =-1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+222}{2*24}=\frac{432}{48} =9 $
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