3/4x-9=-27-3/7x

Solution for 3/4x-9=-27-3/7x equation:

3/4x-9=-27-3/7x

We move all terms to the left:

3/4x-9-(-27-3/7x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(-3/7x-27)-9=0

We get rid of parentheses

3/4x+3/7x+27-9=0

We calculate fractions


21x/28x^2+12x/28x^2+27-9=0

We add all the numbers together, and all the variables

21x/28x^2+12x/28x^2+18=0

We multiply all the terms by the denominator


21x+12x+18*28x^2=0

We add all the numbers together, and all the variables

33x+18*28x^2=0

Wy multiply elements

504x^2+33x=0

a = 504; b = 33; c = 0;
Δ = b2-4ac
Δ = 332-4·504·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-33}{2*504}=\frac{-66}{1008}
=-11/168
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+33}{2*504}=\frac{0}{1008}
=0
$