-4.5+3/2x=2x-7

Solution for -4.5+3/2x=2x-7 equation:

-4.5+3/2x=2x-7

We move all terms to the left:

-4.5+3/2x-(2x-7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x-2x+7-4.5=0

We multiply all the terms by the denominator


-2x*2x+7*2x-(4.5)*2x+3=0

We multiply parentheses

-2x*2x+7*2x-9x+3=0

Wy multiply elements

-4x^2+14x-9x+3=0

We add all the numbers together, and all the variables

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

a = -4; b = 5; c = +3;
Δ = b2-4ac
Δ = 52-4·(-4)·3
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{73}}{2*-4}=\frac{-5-\sqrt{73}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{73}}{2*-4}=\frac{-5+\sqrt{73}}{-8}
$