392=2(x^2+144)

Solution for 392=2(x^2+144) equation:

392=2(x^2+144)

We move all terms to the left:

392-(2(x^2+144))=0


We calculate terms in parentheses: -(2(x^2+144)), so:

2(x^2+144)

We multiply parentheses

2x^2+288

Back to the equation:

-(2x^2+288)


We get rid of parentheses

-2x^2-288+392=0

We add all the numbers together, and all the variables

-2x^2+104=0

a = -2; b = 0; c = +104;
Δ = b2-4ac
Δ = 02-4·(-2)·104
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{13}}{2*-2}=\frac{0-8\sqrt{13}}{-4}
=-\frac{8\sqrt{13}}{-4}
=-\frac{2\sqrt{13}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{13}}{2*-2}=\frac{0+8\sqrt{13}}{-4}
=\frac{8\sqrt{13}}{-4}
=\frac{2\sqrt{13}}{-1}
$