24u=5u^2-5

Solution for 24u=5u^2-5 equation:

24u=5u^2-5

We move all terms to the left:

24u-(5u^2-5)=0

We get rid of parentheses

-5u^2+24u+5=0

a = -5; b = 24; c = +5;
Δ = b2-4ac
Δ = 242-4·(-5)·5
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-26}{2*-5}=\frac{-50}{-10}
=+5
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+26}{2*-5}=\frac{2}{-10}
=-1/5
$