8z+4z^2+2=12

Solution for 8z+4z^2+2=12 equation:

8z+4z^2+2=12

We move all terms to the left:

8z+4z^2+2-(12)=0

We add all the numbers together, and all the variables

4z^2+8z-10=0

a = 4; b = 8; c = -10;
Δ = b2-4ac
Δ = 82-4·4·(-10)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{14}}{2*4}=\frac{-8-4\sqrt{14}}{8}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{14}}{2*4}=\frac{-8+4\sqrt{14}}{8}
$