75x+2400=225x-x^2

Solution for 75x+2400=225x-x^2 equation:

75x+2400=225x-x^2

We move all terms to the left:

75x+2400-(225x-x^2)=0

We get rid of parentheses

x^2-225x+75x+2400=0

We add all the numbers together, and all the variables

x^2-150x+2400=0

a = 1; b = -150; c = +2400;
Δ = b2-4ac
Δ = -1502-4·1·2400
Δ = 12900
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:

$\sqrt{\Delta}=\sqrt{12900}=\sqrt{100*129}=\sqrt{100}*\sqrt{129}=10\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-10\sqrt{129}}{2*1}=\frac{150-10\sqrt{129}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+10\sqrt{129}}{2*1}=\frac{150+10\sqrt{129}}{2}
$