1/2*10^2x=12

Solution for 1/2*10^2x=12 equation:

1/2*10^2x=12

We move all terms to the left:

1/2*10^2x-(12)=0


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

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-12*2*10^2x+1=0

Wy multiply elements

-240x^2*1+1=0

Wy multiply elements

-240x^2+1=0

a = -240; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-240)·1
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{15}}{2*-240}=\frac{0-8\sqrt{15}}{-480}
=-\frac{8\sqrt{15}}{-480}
=-\frac{\sqrt{15}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{15}}{2*-240}=\frac{0+8\sqrt{15}}{-480}
=\frac{8\sqrt{15}}{-480}
=\frac{\sqrt{15}}{-60}
$