3/2x+5=4.5x+4

Solution for 3/2x+5=4.5x+4 equation:

3/2x+5=4.5x+4

We move all terms to the left:

3/2x+5-(4.5x+4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x-4.5x-4+5=0

We multiply all the terms by the denominator


-(4.5x)*2x-4*2x+5*2x+3=0

We add all the numbers together, and all the variables

-(+4.5x)*2x-4*2x+5*2x+3=0

We multiply parentheses

-8x^2-4*2x+5*2x+3=0

Wy multiply elements

-8x^2-8x+10x+3=0

We add all the numbers together, and all the variables

-8x^2+2x+3=0

a = -8; b = 2; c = +3;
Δ = b2-4ac
Δ = 22-4·(-8)·3
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10}{2*-8}=\frac{-12}{-16}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*-8}=\frac{8}{-16}
=-1/2
$