5/8*x=100

Solution for 5/8*x=100 equation:

5/8*x=100

We move all terms to the left:

5/8*x-(100)=0


Domain of the equation: 8*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-100*8*x+5=0

Wy multiply elements

-800x*x+5=0

Wy multiply elements

-800x^2+5=0

a = -800; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-800)·5
Δ = 16000
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:

$\sqrt{\Delta}=\sqrt{16000}=\sqrt{1600*10}=\sqrt{1600}*\sqrt{10}=40\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{10}}{2*-800}=\frac{0-40\sqrt{10}}{-1600}
=-\frac{40\sqrt{10}}{-1600}
=-\frac{\sqrt{10}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{10}}{2*-800}=\frac{0+40\sqrt{10}}{-1600}
=\frac{40\sqrt{10}}{-1600}
=\frac{\sqrt{10}}{-40}
$