-4.5x^2+4x+138=0

Solution for -4.5x^2+4x+138=0 equation:

-4.5x^2+4x+138=0

a = -4.5; b = 4; c = +138;
Δ = b2-4ac
Δ = 42-4·(-4.5)·138
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-50}{2*-4.5}=\frac{-54}{-9}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+50}{2*-4.5}=\frac{46}{-9}
=-5+1/9
$