2y^2-24y+54=0

Solution for 2y^2-24y+54=0 equation:

2y^2-24y+54=0

a = 2; b = -24; c = +54;
Δ = b2-4ac
Δ = -242-4·2·54
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12}{2*2}=\frac{12}{4}
=3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12}{2*2}=\frac{36}{4}
=9
$