X2-10x+45=45x

Solution for X2-10x+45=45x equation:

X2-10X+45=45X

We move all terms to the left:

X2-10X+45-(45X)=0

We add all the numbers together, and all the variables

X^2-55X+45=0

a = 1; b = -55; c = +45;
Δ = b2-4ac
Δ = -552-4·1·45
Δ = 2845
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{-(-55)-\sqrt{2845}}{2*1}=\frac{55-\sqrt{2845}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{2845}}{2*1}=\frac{55+\sqrt{2845}}{2}
$