-3/5x=x+17

Solution for -3/5x=x+17 equation:

-3/5x=x+17

We move all terms to the left:

-3/5x-(x+17)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

-3/5x-x-17=0

We multiply all the terms by the denominator


-x*5x-17*5x-3=0

Wy multiply elements

-5x^2-85x-3=0

a = -5; b = -85; c = -3;
Δ = b2-4ac
Δ = -852-4·(-5)·(-3)
Δ = 7165
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{-(-85)-\sqrt{7165}}{2*-5}=\frac{85-\sqrt{7165}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85)+\sqrt{7165}}{2*-5}=\frac{85+\sqrt{7165}}{-10}
$