30*x-x^2-5^3=0

Solution for 30*x-x^2-5^3=0 equation:

30x-x^2-5^3=0

We add all the numbers together, and all the variables

-1x^2+30x-125=0

a = -1; b = 30; c = -125;
Δ = b2-4ac
Δ = 302-4·(-1)·(-125)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-20}{2*-1}=\frac{-50}{-2}
=+25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+20}{2*-1}=\frac{-10}{-2}
=+5
$