54x^2-102x+40=0

Solution for 54x^2-102x+40=0 equation:

54x^2-102x+40=0

a = 54; b = -102; c = +40;
Δ = b2-4ac
Δ = -1022-4·54·40
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-42}{2*54}=\frac{60}{108}
=5/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+42}{2*54}=\frac{144}{108}
=1+1/3
$