1/163x+5=1/64x+4

Solution for 1/163x+5=1/64x+4 equation:

1/163x+5=1/64x+4

We move all terms to the left:

1/163x+5-(1/64x+4)=0


Domain of the equation: 163x!=0

x!=0/163

x!=0

x∈R



Domain of the equation: 64x+4)!=0

x∈R


We get rid of parentheses

1/163x-1/64x-4+5=0

We calculate fractions


64x/10432x^2+(-163x)/10432x^2-4+5=0

We add all the numbers together, and all the variables

64x/10432x^2+(-163x)/10432x^2+1=0

We multiply all the terms by the denominator


64x+(-163x)+1*10432x^2=0

Wy multiply elements

10432x^2+64x+(-163x)=0

We get rid of parentheses

10432x^2+64x-163x=0

We add all the numbers together, and all the variables

10432x^2-99x=0

a = 10432; b = -99; c = 0;
Δ = b2-4ac
Δ = -992-4·10432·0
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-99}{2*10432}=\frac{0}{20864}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+99}{2*10432}=\frac{198}{20864}
=99/10432
$