7/6x-4=9/4x-6

Solution for 7/6x-4=9/4x-6 equation:

7/6x-4=9/4x-6

We move all terms to the left:

7/6x-4-(9/4x-6)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 4x-6)!=0

x∈R


We get rid of parentheses

7/6x-9/4x+6-4=0

We calculate fractions


28x/24x^2+(-54x)/24x^2+6-4=0

We add all the numbers together, and all the variables

28x/24x^2+(-54x)/24x^2+2=0

We multiply all the terms by the denominator


28x+(-54x)+2*24x^2=0

Wy multiply elements

48x^2+28x+(-54x)=0

We get rid of parentheses

48x^2+28x-54x=0

We add all the numbers together, and all the variables

48x^2-26x=0

a = 48; b = -26; c = 0;
Δ = b2-4ac
Δ = -262-4·48·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-26}{2*48}=\frac{0}{96}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+26}{2*48}=\frac{52}{96}
=13/24
$