1/2*10^2x=50

Solution for 1/2*10^2x=50 equation:

1/2*10^2x=50

We move all terms to the left:

1/2*10^2x-(50)=0


Domain of the equation: 2*10^2x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-50*2*10^2x+1=0

Wy multiply elements

-1000x^2*1+1=0

Wy multiply elements

-1000x^2+1=0

a = -1000; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-1000)·1
Δ = 4000
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:

$\sqrt{\Delta}=\sqrt{4000}=\sqrt{400*10}=\sqrt{400}*\sqrt{10}=20\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{10}}{2*-1000}=\frac{0-20\sqrt{10}}{-2000}
=-\frac{20\sqrt{10}}{-2000}
=-\frac{\sqrt{10}}{-100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{10}}{2*-1000}=\frac{0+20\sqrt{10}}{-2000}
=\frac{20\sqrt{10}}{-2000}
=\frac{\sqrt{10}}{-100}
$