12z2-10z-19=-7

Solution for 12z2-10z-19=-7 equation:

12z^2-10z-19=-7

We move all terms to the left:

12z^2-10z-19-(-7)=0

We add all the numbers together, and all the variables

12z^2-10z-12=0

a = 12; b = -10; c = -12;
Δ = b2-4ac
Δ = -102-4·12·(-12)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-26}{2*12}=\frac{-16}{24}
=-2/3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+26}{2*12}=\frac{36}{24}
=1+1/2
$