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3(2x+1)(4x+1)=0
We multiply parentheses ..
3(+8x^2+2x+4x+1)=0
We multiply parentheses
24x^2+6x+12x+3=0
We add all the numbers together, and all the variables
24x^2+18x+3=0
a = 24; b = 18; c = +3;
Δ = b2-4ac
Δ = 182-4·24·3
Δ = 36
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{36}=6$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6}{2*24}=\frac{-24}{48} =-1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6}{2*24}=\frac{-12}{48} =-1/4 $
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