5/2x-2(4-x)=3

Solution for 5/2x-2(4-x)=3 equation:

5/2x-2(4-x)=3

We move all terms to the left:

5/2x-2(4-x)-(3)=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-2(-1x+4)-3=0

We multiply parentheses

5/2x+2x-8-3=0

We multiply all the terms by the denominator


2x*2x-8*2x-3*2x+5=0

Wy multiply elements

4x^2-16x-6x+5=0

We add all the numbers together, and all the variables

4x^2-22x+5=0

a = 4; b = -22; c = +5;
Δ = b2-4ac
Δ = -222-4·4·5
Δ = 404
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:

$\sqrt{\Delta}=\sqrt{404}=\sqrt{4*101}=\sqrt{4}*\sqrt{101}=2\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{101}}{2*4}=\frac{22-2\sqrt{101}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{101}}{2*4}=\frac{22+2\sqrt{101}}{8}
$