1/2(6x)^2+4=226

Solution for 1/2(6x)^2+4=226 equation:

1/2(6x)^2+4=226

We move all terms to the left:

1/2(6x)^2+4-(226)=0


Domain of the equation: 26x^2!=0

x^2!=0/26

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

1/26x^2-222=0

We multiply all the terms by the denominator


-222*26x^2+1=0

Wy multiply elements

-5772x^2+1=0

a = -5772; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-5772)·1
Δ = 23088
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:

$\sqrt{\Delta}=\sqrt{23088}=\sqrt{16*1443}=\sqrt{16}*\sqrt{1443}=4\sqrt{1443}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{1443}}{2*-5772}=\frac{0-4\sqrt{1443}}{-11544}
=-\frac{4\sqrt{1443}}{-11544}
=-\frac{\sqrt{1443}}{-2886}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{1443}}{2*-5772}=\frac{0+4\sqrt{1443}}{-11544}
=\frac{4\sqrt{1443}}{-11544}
=\frac{\sqrt{1443}}{-2886}
$