1/5x+4x+3(x-5)=x

Solution for 1/5x+4x+3(x-5)=x equation:

1/5x+4x+3(x-5)=x

We move all terms to the left:

1/5x+4x+3(x-5)-(x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

3x+1/5x+3x-15=0

We multiply all the terms by the denominator


3x*5x+3x*5x-15*5x+1=0

Wy multiply elements

15x^2+15x^2-75x+1=0

We add all the numbers together, and all the variables

30x^2-75x+1=0

a = 30; b = -75; c = +1;
Δ = b2-4ac
Δ = -752-4·30·1
Δ = 5505
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{-(-75)-\sqrt{5505}}{2*30}=\frac{75-\sqrt{5505}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+\sqrt{5505}}{2*30}=\frac{75+\sqrt{5505}}{60}
$