1/10x+50=x-13

Solution for 1/10x+50=x-13 equation:

1/10x+50=x-13

We move all terms to the left:

1/10x+50-(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+50=0

We multiply all the terms by the denominator


-x*10x+13*10x+50*10x+1=0

Wy multiply elements

-10x^2+130x+500x+1=0

We add all the numbers together, and all the variables

-10x^2+630x+1=0

a = -10; b = 630; c = +1;
Δ = b2-4ac
Δ = 6302-4·(-10)·1
Δ = 396940
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:

$\sqrt{\Delta}=\sqrt{396940}=\sqrt{4*99235}=\sqrt{4}*\sqrt{99235}=2\sqrt{99235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(630)-2\sqrt{99235}}{2*-10}=\frac{-630-2\sqrt{99235}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(630)+2\sqrt{99235}}{2*-10}=\frac{-630+2\sqrt{99235}}{-20}
$