12z2-44z=45

Solution for 12z2-44z=45 equation:

12z^2-44z=45

We move all terms to the left:

12z^2-44z-(45)=0

a = 12; b = -44; c = -45;
Δ = b2-4ac
Δ = -442-4·12·(-45)
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-64}{2*12}=\frac{-20}{24}
=-5/6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+64}{2*12}=\frac{108}{24}
=4+1/2
$