3X^2+x^2=152^2

Solution for 3X^2+x^2=152^2 equation:

3X^2+X^2=152^2

We move all terms to the left:

3X^2+X^2-(152^2)=0

We add all the numbers together, and all the variables

4X^2-23104=0

a = 4; b = 0; c = -23104;
Δ = b2-4ac
Δ = 02-4·4·(-23104)
Δ = 369664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{369664}=608$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-608}{2*4}=\frac{-608}{8}
=-76
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+608}{2*4}=\frac{608}{8}
=76
$