24z*z=1476

Solution for 24z*z=1476 equation:

24z*z=1476

We move all terms to the left:

24z*z-(1476)=0

Wy multiply elements

24z^2-1476=0

a = 24; b = 0; c = -1476;
Δ = b2-4ac
Δ = 02-4·24·(-1476)
Δ = 141696
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{141696}=\sqrt{576*246}=\sqrt{576}*\sqrt{246}=24\sqrt{246}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{246}}{2*24}=\frac{0-24\sqrt{246}}{48}
=-\frac{24\sqrt{246}}{48}
=-\frac{\sqrt{246}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{246}}{2*24}=\frac{0+24\sqrt{246}}{48}
=\frac{24\sqrt{246}}{48}
=\frac{\sqrt{246}}{2}
$