3/4(2x-7)=-1/8(5-2x)

Solution for 3/4(2x-7)=-1/8(5-2x) equation:

3/4(2x-7)=-1/8(5-2x)

We move all terms to the left:

3/4(2x-7)-(-1/8(5-2x))=0


Domain of the equation: 4(2x-7)!=0

x∈R



Domain of the equation: 8(5-2x))!=0

x∈R


We add all the numbers together, and all the variables

3/4(2x-7)-(-1/8(-2x+5))=0

We calculate fractions


(24x(-)/(4(2x-7)*8(-2x+5)))+(-(-4x2)/(4(2x-7)*8(-2x+5)))=0


We calculate terms in parentheses: +(24x(-)/(4(2x-7)*8(-2x+5))), so:

24x(-)/(4(2x-7)*8(-2x+5))

We add all the numbers together, and all the variables

24x0/(4(2x-7)*8(-2x+5))

We multiply all the terms by the denominator


24x0

We add all the numbers together, and all the variables

24x

Back to the equation:

+(24x)



We calculate terms in parentheses: +(-(-4x2)/(4(2x-7)*8(-2x+5))), so:

-(-4x2)/(4(2x-7)*8(-2x+5))

We add all the numbers together, and all the variables

-(-4x^2)/(4(2x-7)*8(-2x+5))

We multiply all the terms by the denominator


-(-4x^2)

We get rid of parentheses

4x^2

Back to the equation:

+(4x^2)


determiningTheFunctionDomain
4x^2+24x=0

a = 4; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·4·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*4}=\frac{-48}{8}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*4}=\frac{0}{8}
=0
$