z(12z-7)=10

Solution for z(12z-7)=10 equation:

z(12z-7)=10

We move all terms to the left:

z(12z-7)-(10)=0

We multiply parentheses

12z^2-7z-10=0

a = 12; b = -7; c = -10;
Δ = b2-4ac
Δ = -72-4·12·(-10)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-23}{2*12}=\frac{-16}{24}
=-2/3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+23}{2*12}=\frac{30}{24}
=1+1/4
$