2x^2-12x+1/2=0

Solution for 2x^2-12x+1/2=0 equation:

2x^2-12x+1/2=0

We multiply all the terms by the denominator


2x^2*2-12x*2+1=0

Wy multiply elements

4x^2-24x+1=0

a = 4; b = -24; c = +1;
Δ = b2-4ac
Δ = -242-4·4·1
Δ = 560
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:

$\sqrt{\Delta}=\sqrt{560}=\sqrt{16*35}=\sqrt{16}*\sqrt{35}=4\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{35}}{2*4}=\frac{24-4\sqrt{35}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{35}}{2*4}=\frac{24+4\sqrt{35}}{8}
$