3y^2-y-(1/2)=0

Solution for 3y^2-y-(1/2)=0 equation:

3y^2-y-(1/2)=0

We add all the numbers together, and all the variables

3y^2-y-(+1/2)=0

We add all the numbers together, and all the variables

3y^2-1y-(+1/2)=0

We get rid of parentheses

3y^2-1y-1/2=0

We multiply all the terms by the denominator


3y^2*2-1y*2-1=0

Wy multiply elements

6y^2-2y-1=0

a = 6; b = -2; c = -1;
Δ = b2-4ac
Δ = -22-4·6·(-1)
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{7}}{2*6}=\frac{2-2\sqrt{7}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{7}}{2*6}=\frac{2+2\sqrt{7}}{12}
$