30x-x^2-210=0

Solution for 30x-x^2-210=0 equation:

30x-x^2-210=0

We add all the numbers together, and all the variables

-1x^2+30x-210=0

a = -1; b = 30; c = -210;
Δ = b2-4ac
Δ = 302-4·(-1)·(-210)
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{15}}{2*-1}=\frac{-30-2\sqrt{15}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{15}}{2*-1}=\frac{-30+2\sqrt{15}}{-2}
$