7+3/2x+4=4x-5/2x

Solution for 7+3/2x+4=4x-5/2x equation:

7+3/2x+4=4x-5/2x

We move all terms to the left:

7+3/2x+4-(4x-5/2x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/2x-(+4x-5/2x)+7+4=0

We add all the numbers together, and all the variables

3/2x-(+4x-5/2x)+11=0

We get rid of parentheses

3/2x-4x+5/2x+11=0

We multiply all the terms by the denominator


-4x*2x+11*2x+3+5=0

We add all the numbers together, and all the variables

-4x*2x+11*2x+8=0

Wy multiply elements

-8x^2+22x+8=0

a = -8; b = 22; c = +8;
Δ = b2-4ac
Δ = 222-4·(-8)·8
Δ = 740
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:

$\sqrt{\Delta}=\sqrt{740}=\sqrt{4*185}=\sqrt{4}*\sqrt{185}=2\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{185}}{2*-8}=\frac{-22-2\sqrt{185}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{185}}{2*-8}=\frac{-22+2\sqrt{185}}{-16}
$