2(y^2-17y+72)=0

Solution for 2(y^2-17y+72)=0 equation:

2(y^2-17y+72)=0

We multiply parentheses

2y^2-34y+144=0

a = 2; b = -34; c = +144;
Δ = b2-4ac
Δ = -342-4·2·144
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2}{2*2}=\frac{32}{4}
=8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2}{2*2}=\frac{36}{4}
=9
$