-4x+x=6+1/5x

Solution for -4x+x=6+1/5x equation:

-4x+x=6+1/5x

We move all terms to the left:

-4x+x-(6+1/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-4x+x-(1/5x+6)=0

We add all the numbers together, and all the variables

-3x-(1/5x+6)=0

We get rid of parentheses

-3x-1/5x-6=0

We multiply all the terms by the denominator


-3x*5x-6*5x-1=0

Wy multiply elements

-15x^2-30x-1=0

a = -15; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·(-15)·(-1)
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{210}}{2*-15}=\frac{30-2\sqrt{210}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{210}}{2*-15}=\frac{30+2\sqrt{210}}{-30}
$