75/500(.5)=x

Solution for 75/500(.5)=x equation:

75/500(.5)=x

We move all terms to the left:

75/500(.5)-(x)=0

We add all the numbers together, and all the variables

-x+75/500(0.5)=0

We add all the numbers together, and all the variables

-1x+75/500(0.5)=0

We multiply all the terms by the denominator


-1x*500(0.5)+75=0

Wy multiply elements

-500x^2+75=0

a = -500; b = 0; c = +75;
Δ = b2-4ac
Δ = 02-4·(-500)·75
Δ = 150000
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:

$\sqrt{\Delta}=\sqrt{150000}=\sqrt{10000*15}=\sqrt{10000}*\sqrt{15}=100\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{15}}{2*-500}=\frac{0-100\sqrt{15}}{-1000}
=-\frac{100\sqrt{15}}{-1000}
=-\frac{\sqrt{15}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{15}}{2*-500}=\frac{0+100\sqrt{15}}{-1000}
=\frac{100\sqrt{15}}{-1000}
=\frac{\sqrt{15}}{-10}
$