3y+14y^2-6y^2-9y+1-y-3y=0

Solution for 3y+14y^2-6y^2-9y+1-y-3y=0 equation:

3y+14y^2-6y^2-9y+1-y-3y=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 = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{17}}{2*8}=\frac{10-2\sqrt{17}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{17}}{2*8}=\frac{10+2\sqrt{17}}{16}
$