50x^2=x2+5

Solution for 50x^2=x2+5 equation:

50x^2=x2+5

We move all terms to the left:

50x^2-(x2+5)=0

We add all the numbers together, and all the variables

50x^2-(+x^2+5)=0

We get rid of parentheses

50x^2-x^2-5=0

We add all the numbers together, and all the variables

49x^2-5=0

a = 49; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·49·(-5)
Δ = 980
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:

$\sqrt{\Delta}=\sqrt{980}=\sqrt{196*5}=\sqrt{196}*\sqrt{5}=14\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{5}}{2*49}=\frac{0-14\sqrt{5}}{98}
=-\frac{14\sqrt{5}}{98}
=-\frac{\sqrt{5}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{5}}{2*49}=\frac{0+14\sqrt{5}}{98}
=\frac{14\sqrt{5}}{98}
=\frac{\sqrt{5}}{7}
$