5+4x=3/2x

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

5+4x=3/2x

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

4x-3/2x+5=0

We multiply all the terms by the denominator


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

Wy multiply elements

8x^2+10x-3=0

a = 8; b = 10; c = -3;
Δ = b2-4ac
Δ = 102-4·8·(-3)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-14}{2*8}=\frac{-24}{16}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+14}{2*8}=\frac{4}{16}
=1/4
$