23x^2=2(200-x^2)

Solution for 23x^2=2(200-x^2) equation:

23x^2=2(200-x^2)

We move all terms to the left:

23x^2-(2(200-x^2))=0


We calculate terms in parentheses: -(2(200-x^2)), so:

2(200-x^2)

We multiply parentheses

-2x^2+400

Back to the equation:

-(-2x^2+400)


We get rid of parentheses

23x^2+2x^2-400=0

We add all the numbers together, and all the variables

25x^2-400=0

a = 25; b = 0; c = -400;
Δ = b2-4ac
Δ = 02-4·25·(-400)
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200}{2*25}=\frac{-200}{50}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200}{2*25}=\frac{200}{50}
=4
$