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

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

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

We move all terms to the left:

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


Domain of the equation: 1x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


4x/2x^2+5x/2x^2-1=0

We multiply all the terms by the denominator


4x+5x-1*2x^2=0

We add all the numbers together, and all the variables

9x-1*2x^2=0

Wy multiply elements

-2x^2+9x=0

a = -2; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-2)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-2}=\frac{-18}{-4}
=4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-2}=\frac{0}{-4}
=0
$