1/5x=x-22

Solution for 1/5x=x-22 equation:

1/5x=x-22

We move all terms to the left:

1/5x-(x-22)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-x+22=0

We multiply all the terms by the denominator


-x*5x+22*5x+1=0

Wy multiply elements

-5x^2+110x+1=0

a = -5; b = 110; c = +1;
Δ = b2-4ac
Δ = 1102-4·(-5)·1
Δ = 12120
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:

$\sqrt{\Delta}=\sqrt{12120}=\sqrt{4*3030}=\sqrt{4}*\sqrt{3030}=2\sqrt{3030}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-2\sqrt{3030}}{2*-5}=\frac{-110-2\sqrt{3030}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+2\sqrt{3030}}{2*-5}=\frac{-110+2\sqrt{3030}}{-10}
$