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(4x-1)(6x+3)=0
We multiply parentheses ..
(+24x^2+12x-6x-3)=0
We get rid of parentheses
24x^2+12x-6x-3=0
We add all the numbers together, and all the variables
24x^2+6x-3=0
a = 24; b = 6; c = -3;
Δ = b2-4ac
Δ = 62-4·24·(-3)
Δ = 324
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{324}=18$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-18}{2*24}=\frac{-24}{48} =-1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+18}{2*24}=\frac{12}{48} =1/4 $
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