3/4(-X+3)=-3/8(2x-6)

Solution for 3/4(-X+3)=-3/8(2x-6) equation:

3/4(-X+3)=-3/8(2X-6)

We move all terms to the left:

3/4(-X+3)-(-3/8(2X-6))=0


Domain of the equation: 4(-X+3)!=0

X∈R



Domain of the equation: 8(2X-6))!=0

X∈R


We add all the numbers together, and all the variables

3/4(-1X+3)-(-3/8(2X-6))=0

We calculate fractions


(24X2/(4(-1X+3)*8(2X-6)))+(-(-12X0)/(4(-1X+3)*8(2X-6)))=0


We calculate terms in parentheses: +(24X2/(4(-1X+3)*8(2X-6))), so:

24X2/(4(-1X+3)*8(2X-6))

We multiply all the terms by the denominator


24X2

We add all the numbers together, and all the variables

24X^2

Back to the equation:

+(24X^2)



We calculate terms in parentheses: +(-(-12X0)/(4(-1X+3)*8(2X-6))), so:

-(-12X0)/(4(-1X+3)*8(2X-6))

We add all the numbers together, and all the variables

-(-12X)/(4(-1X+3)*8(2X-6))

We multiply all the terms by the denominator


-(-12X)

We get rid of parentheses

12X

Back to the equation:

+(12X)


a = 24; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·24·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*24}=\frac{-24}{48}
=-1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*24}=\frac{0}{48}
=0
$