6z+55(-2z-7)z=1

Solution for 6z+55(-2z-7)z=1 equation:

6z+55(-2z-7)z=1

We move all terms to the left:

6z+55(-2z-7)z-(1)=0

We multiply parentheses

-110z^2+6z-385z-1=0

We add all the numbers together, and all the variables

-110z^2-379z-1=0

a = -110; b = -379; c = -1;
Δ = b2-4ac
Δ = -3792-4·(-110)·(-1)
Δ = 143201
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{-(-379)-\sqrt{143201}}{2*-110}=\frac{379-\sqrt{143201}}{-220}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-379)+\sqrt{143201}}{2*-110}=\frac{379+\sqrt{143201}}{-220}
$