1/5x+10=x

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

1/5x+10=x

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-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}
$