3j^2-13j=-12

Solution for 3j^2-13j=-12 equation:

3j^2-13j=-12

We move all terms to the left:

3j^2-13j-(-12)=0

We add all the numbers together, and all the variables

3j^2-13j+12=0

a = 3; b = -13; c = +12;
Δ = b2-4ac
Δ = -132-4·3·12
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-5}{2*3}=\frac{8}{6}
=1+1/3
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+5}{2*3}=\frac{18}{6}
=3
$