14y^2-5y^2-7y-7y+14-11=0

Solution for 14y^2-5y^2-7y-7y+14-11=0 equation:

14y^2-5y^2-7y-7y+14-11=0

We add all the numbers together, and all the variables

9y^2-14y+3=0

a = 9; b = -14; c = +3;
Δ = b2-4ac
Δ = -142-4·9·3
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{22}}{2*9}=\frac{14-2\sqrt{22}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{22}}{2*9}=\frac{14+2\sqrt{22}}{18}
$