2z(5z+2)=-15z-6

Solution for 2z(5z+2)=-15z-6 equation:

2z(5z+2)=-15z-6

We move all terms to the left:

2z(5z+2)-(-15z-6)=0

We multiply parentheses

10z^2+4z-(-15z-6)=0

We get rid of parentheses

10z^2+4z+15z+6=0

We add all the numbers together, and all the variables

10z^2+19z+6=0

a = 10; b = 19; c = +6;
Δ = b2-4ac
Δ = 192-4·10·6
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-11}{2*10}=\frac{-30}{20}
=-1+1/2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+11}{2*10}=\frac{-8}{20}
=-2/5
$