2x+4/5x+x=92-4/5x

Solution for 2x+4/5x+x=92-4/5x equation:

2x+4/5x+x=92-4/5x

We move all terms to the left:

2x+4/5x+x-(92-4/5x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x+4/5x+x-(-4/5x+92)=0

We add all the numbers together, and all the variables

3x+4/5x-(-4/5x+92)=0

We get rid of parentheses

3x+4/5x+4/5x-92=0

We multiply all the terms by the denominator


3x*5x-92*5x+4+4=0

We add all the numbers together, and all the variables

3x*5x-92*5x+8=0

Wy multiply elements

15x^2-460x+8=0

a = 15; b = -460; c = +8;
Δ = b2-4ac
Δ = -4602-4·15·8
Δ = 211120
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:

$\sqrt{\Delta}=\sqrt{211120}=\sqrt{16*13195}=\sqrt{16}*\sqrt{13195}=4\sqrt{13195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-460)-4\sqrt{13195}}{2*15}=\frac{460-4\sqrt{13195}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-460)+4\sqrt{13195}}{2*15}=\frac{460+4\sqrt{13195}}{30}
$