2/5x+16/5=5/2x-1

Solution for 2/5x+16/5=5/2x-1 equation:

2/5x+16/5=5/2x-1

We move all terms to the left:

2/5x+16/5-(5/2x-1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

2/5x-5/2x+1+16/5=0

We calculate fractions


4x/250x^2+(-625x)/250x^2+32x/250x^2+1=0

We multiply all the terms by the denominator


4x+(-625x)+32x+1*250x^2=0

We add all the numbers together, and all the variables

36x+(-625x)+1*250x^2=0

Wy multiply elements

250x^2+36x+(-625x)=0

We get rid of parentheses

250x^2+36x-625x=0

We add all the numbers together, and all the variables

250x^2-589x=0

a = 250; b = -589; c = 0;
Δ = b2-4ac
Δ = -5892-4·250·0
Δ = 346921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{346921}=589$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-589)-589}{2*250}=\frac{0}{500}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-589)+589}{2*250}=\frac{1178}{500}
=2+89/250
$