x(3x-1)/2=12

Solution for x(3x-1)/2=12 equation:

x(3x-1)/2=12

We move all terms to the left:

x(3x-1)/2-(12)=0

We multiply all the terms by the denominator


x(3x-1)-12*2=0

We add all the numbers together, and all the variables

x(3x-1)-24=0

We multiply parentheses

3x^2-1x-24=0

a = 3; b = -1; c = -24;
Δ = b2-4ac
Δ = -12-4·3·(-24)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-17}{2*3}=\frac{-16}{6}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+17}{2*3}=\frac{18}{6}
=3
$