21/5x-45=x

Solution for 21/5x-45=x equation:

21/5x-45=x

We move all terms to the left:

21/5x-45-(x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+21/5x-45=0

We multiply all the terms by the denominator


-1x*5x-45*5x+21=0

Wy multiply elements

-5x^2-225x+21=0

a = -5; b = -225; c = +21;
Δ = b2-4ac
Δ = -2252-4·(-5)·21
Δ = 51045
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{-(-225)-\sqrt{51045}}{2*-5}=\frac{225-\sqrt{51045}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-225)+\sqrt{51045}}{2*-5}=\frac{225+\sqrt{51045}}{-10}
$