2z^2-8z-2z=6

Solution for 2z^2-8z-2z=6 equation:

2z^2-8z-2z=6

We move all terms to the left:

2z^2-8z-2z-(6)=0

We add all the numbers together, and all the variables

2z^2-10z-6=0

a = 2; b = -10; c = -6;
Δ = b2-4ac
Δ = -102-4·2·(-6)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{37}}{2*2}=\frac{10-2\sqrt{37}}{4}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{37}}{2*2}=\frac{10+2\sqrt{37}}{4}
$