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

Solution for 3(3-2x)=4+(5-x)-1/2x equation:

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

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

-6x-(4+(-1x+5)-1/2x)+9=0

We multiply all the terms by the denominator


-6x*2x)-(4+(-1x+5)+9*2x)-1=0

Wy multiply elements

-12x^2+(-1x+5)+18x=0

We get rid of parentheses

-12x^2-1x+18x+5=0

We add all the numbers together, and all the variables

-12x^2+17x+5=0

a = -12; b = 17; c = +5;
Δ = b2-4ac
Δ = 172-4·(-12)·5
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-23}{2*-12}=\frac{-40}{-24}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+23}{2*-12}=\frac{6}{-24}
=-1/4
$