11-6x=31/10x

Solution for 11-6x=31/10x equation:

11-6x=31/10x

We move all terms to the left:

11-6x-(31/10x)=0


Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-6x-(+31/10x)+11=0

We get rid of parentheses

-6x-31/10x+11=0

We multiply all the terms by the denominator


-6x*10x+11*10x-31=0

Wy multiply elements

-60x^2+110x-31=0

a = -60; b = 110; c = -31;
Δ = b2-4ac
Δ = 1102-4·(-60)·(-31)
Δ = 4660
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:

$\sqrt{\Delta}=\sqrt{4660}=\sqrt{4*1165}=\sqrt{4}*\sqrt{1165}=2\sqrt{1165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-2\sqrt{1165}}{2*-60}=\frac{-110-2\sqrt{1165}}{-120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+2\sqrt{1165}}{2*-60}=\frac{-110+2\sqrt{1165}}{-120}
$