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(-3x+1)(4x+1)=0
We multiply parentheses ..
(-12x^2-3x+4x+1)=0
We get rid of parentheses
-12x^2-3x+4x+1=0
We add all the numbers together, and all the variables
-12x^2+x+1=0
a = -12; b = 1; c = +1;
Δ = b2-4ac
Δ = 12-4·(-12)·1
Δ = 49
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{49}=7$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7}{2*-12}=\frac{-8}{-24} =1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*-12}=\frac{6}{-24} =-1/4 $
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