.38x^2-2.45x+5.1=9

Solution for .38x^2-2.45x+5.1=9 equation:

.38x^2-2.45x+5.1=9

We move all terms to the left:

.38x^2-2.45x+5.1-(9)=0

We add all the numbers together, and all the variables

.38x^2-2.45x-3.9=0

a = .38; b = -2.45; c = -3.9;
Δ = b2-4ac
Δ = -2.452-4·.38·(-3.9)
Δ = 11.9305
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{-(-2.45)-\sqrt{11.9305}}{2*.38}=\frac{2.45-\sqrt{11.9305}}{0.76}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.45)+\sqrt{11.9305}}{2*.38}=\frac{2.45+\sqrt{11.9305}}{0.76}
$