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

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

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

We move all terms to the left:

-4+1x-(-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

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


x*5x+6*5x-4*5x-1=0

Wy multiply elements

5x^2+30x-20x-1=0

We add all the numbers together, and all the variables

5x^2+10x-1=0

a = 5; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·5·(-1)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{30}}{2*5}=\frac{-10-2\sqrt{30}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{30}}{2*5}=\frac{-10+2\sqrt{30}}{10}
$