8.4x(x-4.5)=-33.6

Solution for 8.4x(x-4.5)=-33.6 equation:

8.4x(x-4.5)=-33.6

We move all terms to the left:

8.4x(x-4.5)-(-33.6)=0

We add all the numbers together, and all the variables

8.4x(x-4.5)+33.6=0

We multiply parentheses

8x^2-36x+33.6=0

a = 8; b = -36; c = +33.6;
Δ = b2-4ac
Δ = -362-4·8·33.6
Δ = 220.8
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{-(-36)-\sqrt{220.8}}{2*8}=\frac{36-\sqrt{220.8}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+\sqrt{220.8}}{2*8}=\frac{36+\sqrt{220.8}}{16}
$