x^2+1/2=65/5

Solution for x^2+1/2=65/5 equation:

x^2+1/2=65/5

We move all terms to the left:

x^2+1/2-(65/5)=0

We add all the numbers together, and all the variables

x^2+1/2-13=0

We add all the numbers together, and all the variables

x^2-13+1/2=0

We multiply all the terms by the denominator


x^2*2+1-13*2=0

We add all the numbers together, and all the variables

x^2*2-25=0

Wy multiply elements

2x^2-25=0

a = 2; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·2·(-25)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{2}}{2*2}=\frac{0-10\sqrt{2}}{4}
=-\frac{10\sqrt{2}}{4}
=-\frac{5\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{2}}{2*2}=\frac{0+10\sqrt{2}}{4}
=\frac{10\sqrt{2}}{4}
=\frac{5\sqrt{2}}{2}
$