2z^2+8z=13=0

Solution for 2z^2+8z=13=0 equation:

2z^2+8z=13=0

We move all terms to the left:

2z^2+8z-(13)=0

a = 2; b = 8; c = -13;
Δ = b2-4ac
Δ = 82-4·2·(-13)
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{42}}{2*2}=\frac{-8-2\sqrt{42}}{4}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{42}}{2*2}=\frac{-8+2\sqrt{42}}{4}
$