9z2=-6z+15

Solution for 9z2=-6z+15 equation:

9z^2=-6z+15

We move all terms to the left:

9z^2-(-6z+15)=0

We get rid of parentheses

9z^2+6z-15=0

a = 9; b = 6; c = -15;
Δ = b2-4ac
Δ = 62-4·9·(-15)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-24}{2*9}=\frac{-30}{18}
=-1+2/3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+24}{2*9}=\frac{18}{18}
=1
$