5z^2+16z+8=0

Solution for 5z^2+16z+8=0 equation:

5z^2+16z+8=0

a = 5; b = 16; c = +8;
Δ = b2-4ac
Δ = 162-4·5·8
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{6}}{2*5}=\frac{-16-4\sqrt{6}}{10}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{6}}{2*5}=\frac{-16+4\sqrt{6}}{10}
$