X/7x-6x=-4/17

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

X/7X-6X=-4/17

We move all terms to the left:

X/7X-6X-(-4/17)=0


Domain of the equation: 7X!=0

X!=0/7

X!=0

X∈R


We add all the numbers together, and all the variables

-6X+X/7X-(-4/17)=0

We get rid of parentheses

-6X+X/7X+4/17=0

We calculate fractions


-6X+17X/119X+28X/119X=0

We multiply all the terms by the denominator


-6X*119X+17X+28X=0

We add all the numbers together, and all the variables

45X-6X*119X=0

Wy multiply elements

-714X^2+45X=0

a = -714; b = 45; c = 0;
Δ = b2-4ac
Δ = 452-4·(-714)·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-45}{2*-714}=\frac{-90}{-1428}
=15/238
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45}{2*-714}=\frac{0}{-1428}
=0
$