4x^2=5-x^2-200x+200

Solution for 4x^2=5-x^2-200x+200 equation:

4x^2=5-x^2-200x+200

We move all terms to the left:

4x^2-(5-x^2-200x+200)=0

We get rid of parentheses

4x^2+x^2+200x-5-200=0

We add all the numbers together, and all the variables

5x^2+200x-205=0

a = 5; b = 200; c = -205;
Δ = b2-4ac
Δ = 2002-4·5·(-205)
Δ = 44100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{44100}=210$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-210}{2*5}=\frac{-410}{10}
=-41
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+210}{2*5}=\frac{10}{10}
=1
$