x^2+3x^2=19^2

Solution for x^2+3x^2=19^2 equation:

x^2+3x^2=19^2

We move all terms to the left:

x^2+3x^2-(19^2)=0

We add all the numbers together, and all the variables

4x^2-361=0

a = 4; b = 0; c = -361;
Δ = b2-4ac
Δ = 02-4·4·(-361)
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-76}{2*4}=\frac{-76}{8}
=-9+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+76}{2*4}=\frac{76}{8}
=9+1/2
$