X^2+4.5x=10^2

Solution for X^2+4.5x=10^2 equation:

X^2+4.5X=10^2

We move all terms to the left:

X^2+4.5X-(10^2)=0

We add all the numbers together, and all the variables

X^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}
$