3/5x+1/4x=81/2

Solution for 3/5x+1/4x=81/2 equation:

3/5x+1/4x=81/2

We move all terms to the left:

3/5x+1/4x-(81/2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x+1/4x-(+81/2)=0

We get rid of parentheses

3/5x+1/4x-81/2=0

We calculate fractions


(-6480x^2)/80x^2+48x/80x^2+20x/80x^2=0

We multiply all the terms by the denominator


(-6480x^2)+48x+20x=0

We add all the numbers together, and all the variables

(-6480x^2)+68x=0

We get rid of parentheses

-6480x^2+68x=0

a = -6480; b = 68; c = 0;
Δ = b2-4ac
Δ = 682-4·(-6480)·0
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-68}{2*-6480}=\frac{-136}{-12960}
=17/1620
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+68}{2*-6480}=\frac{0}{-12960}
=0
$