6x^2-40x+54=0

Solution for 6x^2-40x+54=0 equation:

6x^2-40x+54=0

a = 6; b = -40; c = +54;
Δ = b2-4ac
Δ = -402-4·6·54
Δ = 304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{19}}{2*6}=\frac{40-4\sqrt{19}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{19}}{2*6}=\frac{40+4\sqrt{19}}{12}
$