45x-45/18x-18=x

Solution for 45x-45/18x-18=x equation:

45x-45/18x-18=x

We move all terms to the left:

45x-45/18x-18-(x)=0


Domain of the equation: 18x!=0

x!=0/18

x!=0

x∈R


We add all the numbers together, and all the variables

44x-45/18x-18=0

We multiply all the terms by the denominator


44x*18x-18*18x-45=0

Wy multiply elements

792x^2-324x-45=0

a = 792; b = -324; c = -45;
Δ = b2-4ac
Δ = -3242-4·792·(-45)
Δ = 247536
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{247536}=\sqrt{1296*191}=\sqrt{1296}*\sqrt{191}=36\sqrt{191}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-324)-36\sqrt{191}}{2*792}=\frac{324-36\sqrt{191}}{1584}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-324)+36\sqrt{191}}{2*792}=\frac{324+36\sqrt{191}}{1584}
$