2x+6=3-1/5x

Solution for 2x+6=3-1/5x equation:

2x+6=3-1/5x

We move all terms to the left:

2x+6-(3-1/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(-1/5x+3)+6=0

We get rid of parentheses

2x+1/5x-3+6=0

We multiply all the terms by the denominator


2x*5x-3*5x+6*5x+1=0

Wy multiply elements

10x^2-15x+30x+1=0

We add all the numbers together, and all the variables

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}
$