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

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

5+1/2x=2x-2.5

We move all terms to the left:

5+1/2x-(2x-2.5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-2x+2.5+5=0

We multiply all the terms by the denominator


-2x*2x+(2.5)*2x+5*2x+1=0

We multiply parentheses

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

Wy multiply elements

-4x^2+5x+10x+1=0

We add all the numbers together, and all the variables

-4x^2+15x+1=0

a = -4; b = 15; c = +1;
Δ = b2-4ac
Δ = 152-4·(-4)·1
Δ = 241
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{-(15)-\sqrt{241}}{2*-4}=\frac{-15-\sqrt{241}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{241}}{2*-4}=\frac{-15+\sqrt{241}}{-8}
$