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(3x+1)(4x-2)=0
We multiply parentheses ..
(+12x^2-6x+4x-2)=0
We get rid of parentheses
12x^2-6x+4x-2=0
We add all the numbers together, and all the variables
12x^2-2x-2=0
a = 12; b = -2; c = -2;
Δ = b2-4ac
Δ = -22-4·12·(-2)
Δ = 100
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{100}=10$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*12}=\frac{-8}{24} =-1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*12}=\frac{12}{24} =1/2 $
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