4y^2-2y+6y^2-y^2=7

Solution for 4y^2-2y+6y^2-y^2=7 equation:

4y^2-2y+6y^2-y^2=7

We move all terms to the left:

4y^2-2y+6y^2-y^2-(7)=0

We add all the numbers together, and all the variables

9y^2-2y-7=0

a = 9; b = -2; c = -7;
Δ = b2-4ac
Δ = -22-4·9·(-7)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-16}{2*9}=\frac{-14}{18}
=-7/9
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+16}{2*9}=\frac{18}{18}
=1
$