1/5x-x=88

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

1/5x-x=88

We move all terms to the left:

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

We multiply all the terms by the denominator


-1x*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}
$