3z(5z-8)=63

Solution for 3z(5z-8)=63 equation:

3z(5z-8)=63

We move all terms to the left:

3z(5z-8)-(63)=0

We multiply parentheses

15z^2-24z-63=0

a = 15; b = -24; c = -63;
Δ = b2-4ac
Δ = -242-4·15·(-63)
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-66}{2*15}=\frac{-42}{30}
=-1+2/5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+66}{2*15}=\frac{90}{30}
=3
$