-6x2+55x-9=0

Solution for -6x2+55x-9=0 equation:

-6x^2+55x-9=0

a = -6; b = 55; c = -9;
Δ = b2-4ac
Δ = 552-4·(-6)·(-9)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-53}{2*-6}=\frac{-108}{-12}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+53}{2*-6}=\frac{-2}{-12}
=1/6
$