10+x=5*1/5x+2

Solution for 10+x=5*1/5x+2 equation:

10+x=5*1/5x+2

We move all terms to the left:

10+x-(5*1/5x+2)=0


Domain of the equation: 5x+2)!=0

x∈R


We get rid of parentheses

x-5*1/5x-2+10=0

We multiply all the terms by the denominator


x*5x-2*5x+10*5x-5*1=0

We add all the numbers together, and all the variables

x*5x-2*5x+10*5x-5=0

Wy multiply elements

5x^2-10x+50x-5=0

We add all the numbers together, and all the variables

5x^2+40x-5=0

a = 5; b = 40; c = -5;
Δ = b2-4ac
Δ = 402-4·5·(-5)
Δ = 1700
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:

$\sqrt{\Delta}=\sqrt{1700}=\sqrt{100*17}=\sqrt{100}*\sqrt{17}=10\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-10\sqrt{17}}{2*5}=\frac{-40-10\sqrt{17}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+10\sqrt{17}}{2*5}=\frac{-40+10\sqrt{17}}{10}
$