1/4x-9=27-3/7x

Solution for 1/4x-9=27-3/7x equation:

1/4x-9=27-3/7x

We move all terms to the left:

1/4x-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

1/4x-(-3/7x+27)-9=0

We get rid of parentheses

1/4x+3/7x-27-9=0

We calculate fractions


7x/28x^2+12x/28x^2-27-9=0

We add all the numbers together, and all the variables

7x/28x^2+12x/28x^2-36=0

We multiply all the terms by the denominator


7x+12x-36*28x^2=0

We add all the numbers together, and all the variables

19x-36*28x^2=0

Wy multiply elements

-1008x^2+19x=0

a = -1008; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-1008)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-1008}=\frac{-38}{-2016}
=19/1008
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-1008}=\frac{0}{-2016}
=0
$