x*(1/2*x)=338

Solution for x*(1/2*x)=338 equation:

x(1/2x)=338

We move all terms to the left:

x(1/2x)-(338)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x(+1/2x)-338=0

We multiply parentheses

x^2-338=0

a = 1; b = 0; c = -338;
Δ = b2-4ac
Δ = 02-4·1·(-338)
Δ = 1352
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:

$\sqrt{\Delta}=\sqrt{1352}=\sqrt{676*2}=\sqrt{676}*\sqrt{2}=26\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-26\sqrt{2}}{2*1}=\frac{0-26\sqrt{2}}{2}
=-\frac{26\sqrt{2}}{2}
=-13\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+26\sqrt{2}}{2*1}=\frac{0+26\sqrt{2}}{2}
=\frac{26\sqrt{2}}{2}
=13\sqrt{2}
$