1/5x+13=x-7

Solution for 1/5x+13=x-7 equation:

1/5x+13=x-7

We move all terms to the left:

1/5x+13-(x-7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-x+7+13=0

We multiply all the terms by the denominator


-x*5x+7*5x+13*5x+1=0

Wy multiply elements

-5x^2+35x+65x+1=0

We add all the numbers together, and all the variables

-5x^2+100x+1=0

a = -5; b = 100; c = +1;
Δ = b2-4ac
Δ = 1002-4·(-5)·1
Δ = 10020
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:

$\sqrt{\Delta}=\sqrt{10020}=\sqrt{4*2505}=\sqrt{4}*\sqrt{2505}=2\sqrt{2505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-2\sqrt{2505}}{2*-5}=\frac{-100-2\sqrt{2505}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+2\sqrt{2505}}{2*-5}=\frac{-100+2\sqrt{2505}}{-10}
$