8z^2-12=10z

Solution for 8z^2-12=10z equation:

8z^2-12=10z

We move all terms to the left:

8z^2-12-(10z)=0

a = 8; b = -10; c = -12;
Δ = b2-4ac
Δ = -102-4·8·(-12)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-22}{2*8}=\frac{-12}{16}
=-3/4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+22}{2*8}=\frac{32}{16}
=2
$