18z^2-31z+12=2z^2

Solution for 18z^2-31z+12=2z^2 equation:

18z^2-31z+12=2z^2

We move all terms to the left:

18z^2-31z+12-(2z^2)=0

determiningTheFunctionDomain
18z^2-2z^2-31z+12=0

We add all the numbers together, and all the variables

16z^2-31z+12=0

a = 16; b = -31; c = +12;
Δ = b2-4ac
Δ = -312-4·16·12
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-\sqrt{193}}{2*16}=\frac{31-\sqrt{193}}{32}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{193}}{2*16}=\frac{31+\sqrt{193}}{32}
$