50x^2=213+231

Solution for 50x^2=213+231 equation:

50x^2=213+231

We move all terms to the left:

50x^2-(213+231)=0

We add all the numbers together, and all the variables

50x^2-444=0

a = 50; b = 0; c = -444;
Δ = b2-4ac
Δ = 02-4·50·(-444)
Δ = 88800
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:

$\sqrt{\Delta}=\sqrt{88800}=\sqrt{400*222}=\sqrt{400}*\sqrt{222}=20\sqrt{222}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{222}}{2*50}=\frac{0-20\sqrt{222}}{100}
=-\frac{20\sqrt{222}}{100}
=-\frac{\sqrt{222}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{222}}{2*50}=\frac{0+20\sqrt{222}}{100}
=\frac{20\sqrt{222}}{100}
=\frac{\sqrt{222}}{5}
$