2/5x-5/2x=1/2x-3

Solution for 2/5x-5/2x=1/2x-3 equation:

2/5x-5/2x=1/2x-3

We move all terms to the left:

2/5x-5/2x-(1/2x-3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x-3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


4x/10x^2+(-5x-5)/10x^2+3=0

We multiply all the terms by the denominator


4x+(-5x-5)+3*10x^2=0

Wy multiply elements

30x^2+4x+(-5x-5)=0

We get rid of parentheses

30x^2+4x-5x-5=0

We add all the numbers together, and all the variables

30x^2-1x-5=0

a = 30; b = -1; c = -5;
Δ = b2-4ac
Δ = -12-4·30·(-5)
Δ = 601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{601}}{2*30}=\frac{1-\sqrt{601}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{601}}{2*30}=\frac{1+\sqrt{601}}{60}
$