4x(3x+1)=+2

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Solution for 4x(3x+1)=+2 equation:



4x(3x+1)=+2
We move all terms to the left:
4x(3x+1)-(+2)=0
We add all the numbers together, and all the variables
4x(3x+1)-2=0
We multiply parentheses
12x^2+4x-2=0
a = 12; b = 4; c = -2;
Δ = b2-4ac
Δ = 42-4·12·(-2)
Δ = 112
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{7}}{2*12}=\frac{-4-4\sqrt{7}}{24} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{7}}{2*12}=\frac{-4+4\sqrt{7}}{24} $

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