5/2x+(x-4/2)=11

Solution for 5/2x+(x-4/2)=11 equation:

5/2x+(x-4/2)=11

We move all terms to the left:

5/2x+(x-4/2)-(11)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

5/2x+(x-2)-11=0

We get rid of parentheses

5/2x+x-2-11=0

We multiply all the terms by the denominator


x*2x-2*2x-11*2x+5=0

Wy multiply elements

2x^2-4x-22x+5=0

We add all the numbers together, and all the variables

2x^2-26x+5=0

a = 2; b = -26; c = +5;
Δ = b2-4ac
Δ = -262-4·2·5
Δ = 636
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{636}=\sqrt{4*159}=\sqrt{4}*\sqrt{159}=2\sqrt{159}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{159}}{2*2}=\frac{26-2\sqrt{159}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{159}}{2*2}=\frac{26+2\sqrt{159}}{4}
$