(1/55*x)+x=45

Solution for (1/55*x)+x=45 equation:

(1/55x)+x=45

We move all terms to the left:

(1/55x)+x-(45)=0


Domain of the equation: 55x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/55x)+x-45=0

We add all the numbers together, and all the variables

x+(+1/55x)-45=0

We get rid of parentheses

x+1/55x-45=0

We multiply all the terms by the denominator


x*55x-45*55x+1=0

Wy multiply elements

55x^2-2475x+1=0

a = 55; b = -2475; c = +1;
Δ = b2-4ac
Δ = -24752-4·55·1
Δ = 6125405
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:

$\sqrt{\Delta}=\sqrt{6125405}=\sqrt{169*36245}=\sqrt{169}*\sqrt{36245}=13\sqrt{36245}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2475)-13\sqrt{36245}}{2*55}=\frac{2475-13\sqrt{36245}}{110}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2475)+13\sqrt{36245}}{2*55}=\frac{2475+13\sqrt{36245}}{110}
$