x-1/10x=45

Solution for x-1/10x=45 equation:

x-1/10x=45

We move all terms to the left:

x-1/10x-(45)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We multiply all the terms by the denominator


x*10x-45*10x-1=0

Wy multiply elements

10x^2-450x-1=0

a = 10; b = -450; c = -1;
Δ = b2-4ac
Δ = -4502-4·10·(-1)
Δ = 202540
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:

$\sqrt{\Delta}=\sqrt{202540}=\sqrt{4*50635}=\sqrt{4}*\sqrt{50635}=2\sqrt{50635}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-450)-2\sqrt{50635}}{2*10}=\frac{450-2\sqrt{50635}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-450)+2\sqrt{50635}}{2*10}=\frac{450+2\sqrt{50635}}{20}
$