-6z^2+8z+7=0

Solution for -6z^2+8z+7=0 equation:

-6z^2+8z+7=0

a = -6; b = 8; c = +7;
Δ = b2-4ac
Δ = 82-4·(-6)·7
Δ = 232
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{58}}{2*-6}=\frac{-8-2\sqrt{58}}{-12}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{58}}{2*-6}=\frac{-8+2\sqrt{58}}{-12}
$