8z^2+54z+85=0

Solution for 8z^2+54z+85=0 equation:

8z^2+54z+85=0

a = 8; b = 54; c = +85;
Δ = b2-4ac
Δ = 542-4·8·85
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-14}{2*8}=\frac{-68}{16}
=-4+1/4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+14}{2*8}=\frac{-40}{16}
=-2+1/2
$