6/7x-1/4x=17

Solution for 6/7x-1/4x=17 equation:

6/7x-1/4x=17

We move all terms to the left:

6/7x-1/4x-(17)=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


24x/28x^2+(-7x)/28x^2-17=0

We multiply all the terms by the denominator


24x+(-7x)-17*28x^2=0

Wy multiply elements

-476x^2+24x+(-7x)=0

We get rid of parentheses

-476x^2+24x-7x=0

We add all the numbers together, and all the variables

-476x^2+17x=0

a = -476; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-476)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-476}=\frac{-34}{-952}
=1/28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-476}=\frac{0}{-952}
=0
$