6z^2-7z-5=0

Solution for 6z^2-7z-5=0 equation:

6z^2-7z-5=0

a = 6; b = -7; c = -5;
Δ = b2-4ac
Δ = -72-4·6·(-5)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-13}{2*6}=\frac{-6}{12}
=-1/2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*6}=\frac{20}{12}
=1+2/3
$