1/5x+13=x-170

Solution for 1/5x+13=x-170 equation:

1/5x+13=x-170

We move all terms to the left:

1/5x+13-(x-170)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-x+170+13=0

We multiply all the terms by the denominator


-x*5x+170*5x+13*5x+1=0

Wy multiply elements

-5x^2+850x+65x+1=0

We add all the numbers together, and all the variables

-5x^2+915x+1=0

a = -5; b = 915; c = +1;
Δ = b2-4ac
Δ = 9152-4·(-5)·1
Δ = 837245
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(915)-\sqrt{837245}}{2*-5}=\frac{-915-\sqrt{837245}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(915)+\sqrt{837245}}{2*-5}=\frac{-915+\sqrt{837245}}{-10}
$