289=1/2*2x*x

Solution for 289=1/2*2x*x equation:

289=1/2*2x*x

We move all terms to the left:

289-(1/2*2x*x)=0


Domain of the equation: 2*2x*x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+1/2*2x*x)+289=0

We get rid of parentheses

-1/2*2x*x+289=0

We multiply all the terms by the denominator


289*2*2x*x-1=0

Wy multiply elements

1156x^2*2-1=0

Wy multiply elements

2312x^2-1=0

a = 2312; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·2312·(-1)
Δ = 9248
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:

$\sqrt{\Delta}=\sqrt{9248}=\sqrt{4624*2}=\sqrt{4624}*\sqrt{2}=68\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-68\sqrt{2}}{2*2312}=\frac{0-68\sqrt{2}}{4624}
=-\frac{68\sqrt{2}}{4624}
=-\frac{\sqrt{2}}{68}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+68\sqrt{2}}{2*2312}=\frac{0+68\sqrt{2}}{4624}
=\frac{68\sqrt{2}}{4624}
=\frac{\sqrt{2}}{68}
$