6z+5(-2z+7)z=-1

Solution for 6z+5(-2z+7)z=-1 equation:

6z+5(-2z+7)z=-1

We move all terms to the left:

6z+5(-2z+7)z-(-1)=0

We add all the numbers together, and all the variables

6z+5(-2z+7)z+1=0

We multiply parentheses

-10z^2+6z+35z+1=0

We add all the numbers together, and all the variables

-10z^2+41z+1=0

a = -10; b = 41; c = +1;
Δ = b2-4ac
Δ = 412-4·(-10)·1
Δ = 1721
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{-(41)-\sqrt{1721}}{2*-10}=\frac{-41-\sqrt{1721}}{-20}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+\sqrt{1721}}{2*-10}=\frac{-41+\sqrt{1721}}{-20}
$