1/5x+50=-x+10

Solution for 1/5x+50=-x+10 equation:

1/5x+50=-x+10

We move all terms to the left:

1/5x+50-(-x+10)=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-(-1x+10)+50=0

We get rid of parentheses

1/5x+1x-10+50=0

We multiply all the terms by the denominator


1x*5x-10*5x+50*5x+1=0

Wy multiply elements

5x^2-50x+250x+1=0

We add all the numbers together, and all the variables

5x^2+200x+1=0

a = 5; b = 200; c = +1;
Δ = b2-4ac
Δ = 2002-4·5·1
Δ = 39980
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:

$\sqrt{\Delta}=\sqrt{39980}=\sqrt{4*9995}=\sqrt{4}*\sqrt{9995}=2\sqrt{9995}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-2\sqrt{9995}}{2*5}=\frac{-200-2\sqrt{9995}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+2\sqrt{9995}}{2*5}=\frac{-200+2\sqrt{9995}}{10}
$