6+4/5x=9.10x

Solution for 6+4/5x=9.10x equation:

6+4/5x=9.10x

We move all terms to the left:

6+4/5x-(9.10x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

4/5x-(+9.10x)+6=0

We get rid of parentheses

4/5x-9.10x+6=0

We multiply all the terms by the denominator


-(9.10x)*5x+6*5x+4=0

We add all the numbers together, and all the variables

-(+9.10x)*5x+6*5x+4=0

We multiply parentheses

-45x^2+6*5x+4=0

Wy multiply elements

-45x^2+30x+4=0

a = -45; b = 30; c = +4;
Δ = b2-4ac
Δ = 302-4·(-45)·4
Δ = 1620
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:

$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-18\sqrt{5}}{2*-45}=\frac{-30-18\sqrt{5}}{-90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+18\sqrt{5}}{2*-45}=\frac{-30+18\sqrt{5}}{-90}
$