X^2-4.5x=-2

Solution for X^2-4.5x=-2 equation:

X^2-4.5X=-2

We move all terms to the left:

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

We add all the numbers together, and all the variables

X^2-4.5X+2=0

a = 1; b = -4.5; c = +2;
Δ = b2-4ac
Δ = -4.52-4·1·2
Δ = 12.25
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{12.25}}{2*1}=\frac{4.5-\sqrt{12.25}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4.5)+\sqrt{12.25}}{2*1}=\frac{4.5+\sqrt{12.25}}{2}
$