-1/5x=2x+3

Solution for -1/5x=2x+3 equation:

-1/5x=2x+3

We move all terms to the left:

-1/5x-(2x+3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

-1/5x-2x-3=0

We multiply all the terms by the denominator


-2x*5x-3*5x-1=0

Wy multiply elements

-10x^2-15x-1=0

a = -10; b = -15; c = -1;
Δ = b2-4ac
Δ = -152-4·(-10)·(-1)
Δ = 185
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{-(-15)-\sqrt{185}}{2*-10}=\frac{15-\sqrt{185}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{185}}{2*-10}=\frac{15+\sqrt{185}}{-20}
$