5z^2+24z=5z

Solution for 5z^2+24z=5z equation:

5z^2+24z=5z

We move all terms to the left:

5z^2+24z-(5z)=0

We add all the numbers together, and all the variables

5z^2+19z=0

a = 5; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·5·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*5}=\frac{-38}{10}
=-3+4/5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*5}=\frac{0}{10}
=0
$