100=x^2+4.5x

Solution for 100=x^2+4.5x equation:

100=x^2+4.5x

We move all terms to the left:

100-(x^2+4.5x)=0

We get rid of parentheses

-x^2-4.5x+100=0

We add all the numbers together, and all the variables

-1x^2-4.5x+100=0

a = -1; b = -4.5; c = +100;
Δ = b2-4ac
Δ = -4.52-4·(-1)·100
Δ = 420.25
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{-(-4.5)-\sqrt{420.25}}{2*-1}=\frac{4.5-\sqrt{420.25}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4.5)+\sqrt{420.25}}{2*-1}=\frac{4.5+\sqrt{420.25}}{-2}
$