24z^2+50z^2+24z=0

Solution for 24z^2+50z^2+24z=0 equation:

24z^2+50z^2+24z=0

We add all the numbers together, and all the variables

74z^2+24z=0

a = 74; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·74·0
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{-(24)-24}{2*74}=\frac{-48}{148}
=-12/37
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*74}=\frac{0}{148}
=0
$