(3x+1)(4x-1)=

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Solution for (3x+1)(4x-1)= equation:



(3x+1)(4x-1)=
We move all terms to the left:
(3x+1)(4x-1)-()=0
We add all the numbers together, and all the variables
(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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