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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x+15)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


25x/10x^2+(-4x)/10x^2-15+3=0

We add all the numbers together, and all the variables

25x/10x^2+(-4x)/10x^2-12=0

We multiply all the terms by the denominator


25x+(-4x)-12*10x^2=0

Wy multiply elements

-120x^2+25x+(-4x)=0

We get rid of parentheses

-120x^2+25x-4x=0

We add all the numbers together, and all the variables

-120x^2+21x=0

a = -120; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-120)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-120}=\frac{-42}{-240}
=7/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-120}=\frac{0}{-240}
=0
$