13x^2+1/2=6x

Solution for 13x^2+1/2=6x equation:

13x^2+1/2=6x

We move all terms to the left:

13x^2+1/2-(6x)=0

We multiply all the terms by the denominator


13x^2*2-6x*2+1=0

Wy multiply elements

26x^2-12x+1=0

a = 26; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·26·1
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{10}}{2*26}=\frac{12-2\sqrt{10}}{52}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{10}}{2*26}=\frac{12+2\sqrt{10}}{52}
$