-5/2x+40=5/3x+15

Solution for -5/2x+40=5/3x+15 equation:

-5/2x+40=5/3x+15

We move all terms to the left:

-5/2x+40-(5/3x+15)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x+15)!=0

x∈R


We get rid of parentheses

-5/2x-5/3x-15+40=0

We calculate fractions


(-15x)/6x^2+(-10x)/6x^2-15+40=0

We add all the numbers together, and all the variables

(-15x)/6x^2+(-10x)/6x^2+25=0

We multiply all the terms by the denominator


(-15x)+(-10x)+25*6x^2=0

Wy multiply elements

150x^2+(-15x)+(-10x)=0

We get rid of parentheses

150x^2-15x-10x=0

We add all the numbers together, and all the variables

150x^2-25x=0

a = 150; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·150·0
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*150}=\frac{0}{300}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*150}=\frac{50}{300}
=1/6
$