1/5x+3x=42-2x

Solution for 1/5x+3x=42-2x equation:

1/5x+3x=42-2x

We move all terms to the left:

1/5x+3x-(42-2x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

1/5x+3x-(-2x+42)=0

We add all the numbers together, and all the variables

3x+1/5x-(-2x+42)=0

We get rid of parentheses

3x+1/5x+2x-42=0

We multiply all the terms by the denominator


3x*5x+2x*5x-42*5x+1=0

Wy multiply elements

15x^2+10x^2-210x+1=0

We add all the numbers together, and all the variables

25x^2-210x+1=0

a = 25; b = -210; c = +1;
Δ = b2-4ac
Δ = -2102-4·25·1
Δ = 44000
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:

$\sqrt{\Delta}=\sqrt{44000}=\sqrt{400*110}=\sqrt{400}*\sqrt{110}=20\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-20\sqrt{110}}{2*25}=\frac{210-20\sqrt{110}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+20\sqrt{110}}{2*25}=\frac{210+20\sqrt{110}}{50}
$