60^2+x^2=(4+2x^2)

Solution for 60^2+x^2=(4+2x^2) equation:

60^2+x^2=(4+2x^2)

We move all terms to the left:

60^2+x^2-((4+2x^2))=0

We add all the numbers together, and all the variables

x^2-((4+2x^2))+3600=0


We calculate terms in parentheses: -((4+2x^2)), so:

(4+2x^2)

We get rid of parentheses

2x^2+4

Back to the equation:

-(2x^2+4)


We get rid of parentheses

x^2-2x^2-4+3600=0

We add all the numbers together, and all the variables

-1x^2+3596=0

a = -1; b = 0; c = +3596;
Δ = b2-4ac
Δ = 02-4·(-1)·3596
Δ = 14384
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:

$\sqrt{\Delta}=\sqrt{14384}=\sqrt{16*899}=\sqrt{16}*\sqrt{899}=4\sqrt{899}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{899}}{2*-1}=\frac{0-4\sqrt{899}}{-2}
=-\frac{4\sqrt{899}}{-2}
=-\frac{2\sqrt{899}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{899}}{2*-1}=\frac{0+4\sqrt{899}}{-2}
=\frac{4\sqrt{899}}{-2}
=\frac{2\sqrt{899}}{-1}
$