81x-1=1/2(100x)

Solution for 81x-1=1/2(100x) equation:

81x-1=1/2(100x)

We move all terms to the left:

81x-1-(1/2(100x))=0


Domain of the equation: 2100x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

81x-(+1/2100x)-1=0

We get rid of parentheses

81x-1/2100x-1=0

We multiply all the terms by the denominator


81x*2100x-1*2100x-1=0

Wy multiply elements

170100x^2-2100x-1=0

a = 170100; b = -2100; c = -1;
Δ = b2-4ac
Δ = -21002-4·170100·(-1)
Δ = 5090400
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:

$\sqrt{\Delta}=\sqrt{5090400}=\sqrt{3600*1414}=\sqrt{3600}*\sqrt{1414}=60\sqrt{1414}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2100)-60\sqrt{1414}}{2*170100}=\frac{2100-60\sqrt{1414}}{340200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2100)+60\sqrt{1414}}{2*170100}=\frac{2100+60\sqrt{1414}}{340200}
$