1200-1,5x^2=200+x^2

Solution for 1200-1,5x^2=200+x^2 equation:

1200-1.5x^2=200+x^2

We move all terms to the left:

1200-1.5x^2-(200+x^2)=0

We get rid of parentheses

-1.5x^2-x^2-200+1200=0

We add all the numbers together, and all the variables

-2.5x^2+1000=0

a = -2.5; b = 0; c = +1000;
Δ = b2-4ac
Δ = 02-4·(-2.5)·1000
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100}{2*-2.5}=\frac{-100}{-5}
=+20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100}{2*-2.5}=\frac{100}{-5}
=-20
$