13z=-5-6z2

Solution for 13z=-5-6z2 equation:

13z=-5-6z^2

We move all terms to the left:

13z-(-5-6z^2)=0

We get rid of parentheses

6z^2+13z+5=0

a = 6; b = 13; c = +5;
Δ = b2-4ac
Δ = 132-4·6·5
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-7}{2*6}=\frac{-20}{12}
=-1+2/3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+7}{2*6}=\frac{-6}{12}
=-1/2
$