x^2+4x^2=490

Solution for x^2+4x^2=490 equation:

x^2+4x^2=490

We move all terms to the left:

x^2+4x^2-(490)=0

We add all the numbers together, and all the variables

5x^2-490=0

a = 5; b = 0; c = -490;
Δ = b2-4ac
Δ = 02-4·5·(-490)
Δ = 9800
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:

$\sqrt{\Delta}=\sqrt{9800}=\sqrt{4900*2}=\sqrt{4900}*\sqrt{2}=70\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-70\sqrt{2}}{2*5}=\frac{0-70\sqrt{2}}{10}
=-\frac{70\sqrt{2}}{10}
=-7\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+70\sqrt{2}}{2*5}=\frac{0+70\sqrt{2}}{10}
=\frac{70\sqrt{2}}{10}
=7\sqrt{2}
$