4+x=-6+1/5x

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

4+x=-6+1/5x

We move all terms to the left:

4+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

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+50x-1=0

a = 5; b = 50; c = -1;
Δ = b2-4ac
Δ = 502-4·5·(-1)
Δ = 2520
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:

$\sqrt{\Delta}=\sqrt{2520}=\sqrt{36*70}=\sqrt{36}*\sqrt{70}=6\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-6\sqrt{70}}{2*5}=\frac{-50-6\sqrt{70}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+6\sqrt{70}}{2*5}=\frac{-50+6\sqrt{70}}{10}
$