-12+5(-2z-7)z=-1

Solution for -12+5(-2z-7)z=-1 equation:

-12+5(-2z-7)z=-1

We move all terms to the left:

-12+5(-2z-7)z-(-1)=0

We add all the numbers together, and all the variables

5(-2z-7)z-11=0

We multiply parentheses

-10z^2-35z-11=0

a = -10; b = -35; c = -11;
Δ = b2-4ac
Δ = -352-4·(-10)·(-11)
Δ = 785
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{-(-35)-\sqrt{785}}{2*-10}=\frac{35-\sqrt{785}}{-20}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{785}}{2*-10}=\frac{35+\sqrt{785}}{-20}
$