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 add all the numbers together, and all the variables

x-((1/5x+2))+15=0

We multiply all the terms by the denominator


x*5x+15*5x+2))-((1+2))=0

We add all the numbers together, and all the variables

x*5x+15*5x+2))-(3)=0

We add all the numbers together, and all the variables

x*5x+15*5x=0

Wy multiply elements

5x^2+75x=0

a = 5; b = 75; c = 0;
Δ = b2-4ac
Δ = 752-4·5·0
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-75}{2*5}=\frac{-150}{10}
=-15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+75}{2*5}=\frac{0}{10}
=0
$