1/10x+5=x-13

Solution for 1/10x+5=x-13 equation:

1/10x+5=x-13

We move all terms to the left:

1/10x+5-(x-13)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We get rid of parentheses

1/10x-x+13+5=0

We multiply all the terms by the denominator


-x*10x+13*10x+5*10x+1=0

Wy multiply elements

-10x^2+130x+50x+1=0

We add all the numbers together, and all the variables

-10x^2+180x+1=0

a = -10; b = 180; c = +1;
Δ = b2-4ac
Δ = 1802-4·(-10)·1
Δ = 32440
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:

$\sqrt{\Delta}=\sqrt{32440}=\sqrt{4*8110}=\sqrt{4}*\sqrt{8110}=2\sqrt{8110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-2\sqrt{8110}}{2*-10}=\frac{-180-2\sqrt{8110}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+2\sqrt{8110}}{2*-10}=\frac{-180+2\sqrt{8110}}{-20}
$