2150=105x-300-x^2

Solution for 2150=105x-300-x^2 equation:

2150=105x-300-x^2

We move all terms to the left:

2150-(105x-300-x^2)=0

We get rid of parentheses

x^2-105x+300+2150=0

We add all the numbers together, and all the variables

x^2-105x+2450=0

a = 1; b = -105; c = +2450;
Δ = b2-4ac
Δ = -1052-4·1·2450
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-35}{2*1}=\frac{70}{2}
=35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+35}{2*1}=\frac{140}{2}
=70
$