108x^2-99x+3=0

Solution for 108x^2-99x+3=0 equation:

108x^2-99x+3=0

a = 108; b = -99; c = +3;
Δ = b2-4ac
Δ = -992-4·108·3
Δ = 8505
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:

$\sqrt{\Delta}=\sqrt{8505}=\sqrt{81*105}=\sqrt{81}*\sqrt{105}=9\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-9\sqrt{105}}{2*108}=\frac{99-9\sqrt{105}}{216}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+9\sqrt{105}}{2*108}=\frac{99+9\sqrt{105}}{216}
$