x-1/5x=88

Solution for x-1/5x=88 equation:

x-1/5x=88

We move all terms to the left:

x-1/5x-(88)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


x*5x-88*5x-1=0

Wy multiply elements

5x^2-440x-1=0

a = 5; b = -440; c = -1;
Δ = b2-4ac
Δ = -4402-4·5·(-1)
Δ = 193620
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:

$\sqrt{\Delta}=\sqrt{193620}=\sqrt{4*48405}=\sqrt{4}*\sqrt{48405}=2\sqrt{48405}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-440)-2\sqrt{48405}}{2*5}=\frac{440-2\sqrt{48405}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-440)+2\sqrt{48405}}{2*5}=\frac{440+2\sqrt{48405}}{10}
$