-1/40x+15=-1/15x+31

Solution for -1/40x+15=-1/15x+31 equation:

-1/40x+15=-1/15x+31

We move all terms to the left:

-1/40x+15-(-1/15x+31)=0


Domain of the equation: 40x!=0

x!=0/40

x!=0

x∈R



Domain of the equation: 15x+31)!=0

x∈R


We get rid of parentheses

-1/40x+1/15x-31+15=0

We calculate fractions


(-15x)/600x^2+40x/600x^2-31+15=0

We add all the numbers together, and all the variables

(-15x)/600x^2+40x/600x^2-16=0

We multiply all the terms by the denominator


(-15x)+40x-16*600x^2=0

We add all the numbers together, and all the variables

40x+(-15x)-16*600x^2=0

Wy multiply elements

-9600x^2+40x+(-15x)=0

We get rid of parentheses

-9600x^2+40x-15x=0

We add all the numbers together, and all the variables

-9600x^2+25x=0

a = -9600; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-9600)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-9600}=\frac{-50}{-19200}
=1/384
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-9600}=\frac{0}{-19200}
=0
$