2x+6=31/5x

Solution for 2x+6=31/5x equation:

2x+6=31/5x

We move all terms to the left:

2x+6-(31/5x)=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-(+31/5x)+6=0

We get rid of parentheses

2x-31/5x+6=0

We multiply all the terms by the denominator


2x*5x+6*5x-31=0

Wy multiply elements

10x^2+30x-31=0

a = 10; b = 30; c = -31;
Δ = b2-4ac
Δ = 302-4·10·(-31)
Δ = 2140
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:

$\sqrt{\Delta}=\sqrt{2140}=\sqrt{4*535}=\sqrt{4}*\sqrt{535}=2\sqrt{535}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{535}}{2*10}=\frac{-30-2\sqrt{535}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{535}}{2*10}=\frac{-30+2\sqrt{535}}{20}
$