3x^2-8.25x+1=0

Solution for 3x^2-8.25x+1=0 equation:

3x^2-8.25x+1=0

a = 3; b = -8.25; c = +1;
Δ = b2-4ac
Δ = -8.252-4·3·1
Δ = 56.0625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8.25)-\sqrt{56.0625}}{2*3}=\frac{8.25-\sqrt{56.0625}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8.25)+\sqrt{56.0625}}{2*3}=\frac{8.25+\sqrt{56.0625}}{6}
$