2(y^2-13y+40)=0

Solution for 2(y^2-13y+40)=0 equation:

2(y^2-13y+40)=0

We multiply parentheses

2y^2-26y+80=0

a = 2; b = -26; c = +80;
Δ = b2-4ac
Δ = -262-4·2·80
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-6}{2*2}=\frac{20}{4}
=5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+6}{2*2}=\frac{32}{4}
=8
$