3y^2-2y+6y^2-y^2=6

Solution for 3y^2-2y+6y^2-y^2=6 equation:

3y^2-2y+6y^2-y^2=6

We move all terms to the left:

3y^2-2y+6y^2-y^2-(6)=0

We add all the numbers together, and all the variables

8y^2-2y-6=0

a = 8; b = -2; c = -6;
Δ = b2-4ac
Δ = -22-4·8·(-6)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-14}{2*8}=\frac{-12}{16}
=-3/4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+14}{2*8}=\frac{16}{16}
=1
$