-0.2x^2+1.50x+6=4.5

Solution for -0.2x^2+1.50x+6=4.5 equation:

-0.2x^2+1.50x+6=4.5

We move all terms to the left:

-0.2x^2+1.50x+6-(4.5)=0

We add all the numbers together, and all the variables

-0.2x^2+1.50x+1.5=0

a = -0.2; b = 1.50; c = +1.5;
Δ = b2-4ac
Δ = 1.502-4·(-0.2)·1.5
Δ = 3.45
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{-(1.50)-\sqrt{3.45}}{2*-0.2}=\frac{-1.5-\sqrt{3.45}}{-0.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.50)+\sqrt{3.45}}{2*-0.2}=\frac{-1.5+\sqrt{3.45}}{-0.4}
$