3/4x-5/8=5/162x

Solution for 3/4x-5/8=5/162x equation:

3/4x-5/8=5/162x

We move all terms to the left:

3/4x-5/8-(5/162x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 162x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(+5/162x)-5/8=0

We get rid of parentheses

3/4x-5/162x-5/8=0

We calculate fractions


(-3240x^2)/41472x^2+31104x/41472x^2+(-1280x)/41472x^2=0

We multiply all the terms by the denominator


(-3240x^2)+31104x+(-1280x)=0

We get rid of parentheses

-3240x^2+31104x-1280x=0

We add all the numbers together, and all the variables

-3240x^2+29824x=0

a = -3240; b = 29824; c = 0;
Δ = b2-4ac
Δ = 298242-4·(-3240)·0
Δ = 889470976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{889470976}=29824$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29824)-29824}{2*-3240}=\frac{-59648}{-6480}
=9+83/405
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29824)+29824}{2*-3240}=\frac{0}{-6480}
=0
$