6z(z+4)=-10

Solution for 6z(z+4)=-10 equation:

6z(z+4)=-10

We move all terms to the left:

6z(z+4)-(-10)=0

We add all the numbers together, and all the variables

6z(z+4)+10=0

We multiply parentheses

6z^2+24z+10=0

a = 6; b = 24; c = +10;
Δ = b2-4ac
Δ = 242-4·6·10
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{21}}{2*6}=\frac{-24-4\sqrt{21}}{12}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{21}}{2*6}=\frac{-24+4\sqrt{21}}{12}
$