x^2-(19/6)x+(1/2)=0

Solution for x^2-(19/6)x+(1/2)=0 equation:

x^2-(19/6)x+(1/2)=0


Domain of the equation: 6)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x^2-(+19/6)x+(+1/2)=0

We multiply parentheses

x^2-19x^2+(+1/2)=0

We get rid of parentheses

x^2-19x^2+1/2=0

We multiply all the terms by the denominator


x^2*2-19x^2*2+1=0

Wy multiply elements

2x^2-38x^2+1=0

We add all the numbers together, and all the variables

-36x^2+1=0

a = -36; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-36)·1
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*-36}=\frac{-12}{-72}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*-36}=\frac{12}{-72}
=-1/6
$