3/4(2x-6)=1/2(-3x-9)

Solution for 3/4(2x-6)=1/2(-3x-9) equation:

3/4(2x-6)=1/2(-3x-9)

We move all terms to the left:

3/4(2x-6)-(1/2(-3x-9))=0


Domain of the equation: 4(2x-6)!=0

x∈R



Domain of the equation: 2(-3x-9))!=0

x∈R


We calculate fractions


(6x(-)/(4(2x-6)*2(-3x-9)))+(-4x2/(4(2x-6)*2(-3x-9)))=0


We calculate terms in parentheses: +(6x(-)/(4(2x-6)*2(-3x-9))), so:

6x(-)/(4(2x-6)*2(-3x-9))

We add all the numbers together, and all the variables

6x0/(4(2x-6)*2(-3x-9))

We multiply all the terms by the denominator


6x0

We add all the numbers together, and all the variables

6x

Back to the equation:

+(6x)



We calculate terms in parentheses: +(-4x2/(4(2x-6)*2(-3x-9))), so:

-4x2/(4(2x-6)*2(-3x-9))

We multiply all the terms by the denominator


-4x2

We add all the numbers together, and all the variables

-4x^2

Back to the equation:

+(-4x^2)


We get rid of parentheses

-4x^2+6x=0

a = -4; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-4)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-4}=\frac{-12}{-8}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-4}=\frac{0}{-8}
=0
$