2(y2-2)-9y+14=0

Solution for 2(y2-2)-9y+14=0 equation:

2(y2-2)-9y+14=0

We add all the numbers together, and all the variables

2(+y^2-2)-9y+14=0

We multiply parentheses

2y^2-9y-4+14=0

We add all the numbers together, and all the variables

2y^2-9y+10=0

a = 2; b = -9; c = +10;
Δ = b2-4ac
Δ = -92-4·2·10
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-1}{2*2}=\frac{8}{4}
=2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+1}{2*2}=\frac{10}{4}
=2+1/2
$