6z+5(-2z-7)z=-2

Solution for 6z+5(-2z-7)z=-2 equation:

6z+5(-2z-7)z=-2

We move all terms to the left:

6z+5(-2z-7)z-(-2)=0

We add all the numbers together, and all the variables

6z+5(-2z-7)z+2=0

We multiply parentheses

-10z^2+6z-35z+2=0

We add all the numbers together, and all the variables

-10z^2-29z+2=0

a = -10; b = -29; c = +2;
Δ = b2-4ac
Δ = -292-4·(-10)·2
Δ = 921
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{-(-29)-\sqrt{921}}{2*-10}=\frac{29-\sqrt{921}}{-20}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{921}}{2*-10}=\frac{29+\sqrt{921}}{-20}
$