-3x2+5.5x+1=0

Solution for -3x2+5.5x+1=0 equation:

-3x^2+5.5x+1=0

a = -3; b = 5.5; c = +1;
Δ = b2-4ac
Δ = 5.52-4·(-3)·1
Δ = 42.25
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{-(5.5)-\sqrt{42.25}}{2*-3}=\frac{-5.5-\sqrt{42.25}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5.5)+\sqrt{42.25}}{2*-3}=\frac{-5.5+\sqrt{42.25}}{-6}
$