4/7x-1/4x=9

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

4/7x-1/4x=9

We move all terms to the left:

4/7x-1/4x-(9)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


16x/28x^2+(-7x)/28x^2-9=0

We multiply all the terms by the denominator


16x+(-7x)-9*28x^2=0

Wy multiply elements

-252x^2+16x+(-7x)=0

We get rid of parentheses

-252x^2+16x-7x=0

We add all the numbers together, and all the variables

-252x^2+9x=0

a = -252; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-252)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-252}=\frac{-18}{-504}
=1/28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-252}=\frac{0}{-504}
=0
$