(-6y-2y)-(-3-4y);y=1/2

Solution for (-6y-2y)-(-3-4y);y=1/2 equation:

(-6y-2y)-(-3-4y)y=1/2

We move all terms to the left:

(-6y-2y)-(-3-4y)y-(1/2)=0

We add all the numbers together, and all the variables

(-8y)-(-4y-3)y-(+1/2)=0

We multiply parentheses

4y^2+(-8y)+3y-(+1/2)=0

We get rid of parentheses

4y^2-8y+3y-1/2=0

We multiply all the terms by the denominator


4y^2*2-8y*2+3y*2-1=0

Wy multiply elements

8y^2-16y+6y-1=0

We add all the numbers together, and all the variables

8y^2-10y-1=0

a = 8; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·8·(-1)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{33}}{2*8}=\frac{10-2\sqrt{33}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{33}}{2*8}=\frac{10+2\sqrt{33}}{16}
$