4x^2=50x^2-200x+200

Solution for 4x^2=50x^2-200x+200 equation:

4x^2=50x^2-200x+200

We move all terms to the left:

4x^2-(50x^2-200x+200)=0

We get rid of parentheses

4x^2-50x^2+200x-200=0

We add all the numbers together, and all the variables

-46x^2+200x-200=0

a = -46; b = 200; c = -200;
Δ = b2-4ac
Δ = 2002-4·(-46)·(-200)
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-40\sqrt{2}}{2*-46}=\frac{-200-40\sqrt{2}}{-92}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+40\sqrt{2}}{2*-46}=\frac{-200+40\sqrt{2}}{-92}
$