1x-1/5x=288

Solution for 1x-1/5x=288 equation:

1x-1/5x=288

We move all terms to the left:

1x-1/5x-(288)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

x-1/5x-288=0

We multiply all the terms by the denominator


x*5x-288*5x-1=0

Wy multiply elements

5x^2-1440x-1=0

a = 5; b = -1440; c = -1;
Δ = b2-4ac
Δ = -14402-4·5·(-1)
Δ = 2073620
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:

$\sqrt{\Delta}=\sqrt{2073620}=\sqrt{4*518405}=\sqrt{4}*\sqrt{518405}=2\sqrt{518405}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1440)-2\sqrt{518405}}{2*5}=\frac{1440-2\sqrt{518405}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1440)+2\sqrt{518405}}{2*5}=\frac{1440+2\sqrt{518405}}{10}
$