m^2=300-200m

Solution for m^2=300-200m equation:

m^2=300-200m

We move all terms to the left:

m^2-(300-200m)=0

We add all the numbers together, and all the variables

m^2-(-200m+300)=0

We get rid of parentheses

m^2+200m-300=0

a = 1; b = 200; c = -300;
Δ = b2-4ac
Δ = 2002-4·1·(-300)
Δ = 41200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{41200}=\sqrt{400*103}=\sqrt{400}*\sqrt{103}=20\sqrt{103}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-20\sqrt{103}}{2*1}=\frac{-200-20\sqrt{103}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+20\sqrt{103}}{2*1}=\frac{-200+20\sqrt{103}}{2}
$