12z^2=z+1

Solution for 12z^2=z+1 equation:

12z^2=z+1

We move all terms to the left:

12z^2-(z+1)=0

We get rid of parentheses

12z^2-z-1=0

We add all the numbers together, and all the variables

12z^2-1z-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:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-7}{2*12}=\frac{-6}{24}
=-1/4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+7}{2*12}=\frac{8}{24}
=1/3
$