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 multiply parentheses

5/2x+2x-8-11=0

We multiply all the terms by the denominator


2x*2x-8*2x-11*2x+5=0

Wy multiply elements

4x^2-16x-22x+5=0

We add all the numbers together, and all the variables

4x^2-38x+5=0

a = 4; b = -38; c = +5;
Δ = b2-4ac
Δ = -382-4·4·5
Δ = 1364
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:

$\sqrt{\Delta}=\sqrt{1364}=\sqrt{4*341}=\sqrt{4}*\sqrt{341}=2\sqrt{341}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{341}}{2*4}=\frac{38-2\sqrt{341}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{341}}{2*4}=\frac{38+2\sqrt{341}}{8}
$