7/x-3-4/6x-18=-7

Solution for 7/x-3-4/6x-18=-7 equation:

7/x-3-4/6x-18=-7

We move all terms to the left:

7/x-3-4/6x-18-(-7)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

7/x-4/6x-14=0

We calculate fractions


42x/6x^2+(-4x)/6x^2-14=0

We multiply all the terms by the denominator


42x+(-4x)-14*6x^2=0

Wy multiply elements

-84x^2+42x+(-4x)=0

We get rid of parentheses

-84x^2+42x-4x=0

We add all the numbers together, and all the variables

-84x^2+38x=0

a = -84; b = 38; c = 0;
Δ = b2-4ac
Δ = 382-4·(-84)·0
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-38}{2*-84}=\frac{-76}{-168}
=19/42
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+38}{2*-84}=\frac{0}{-168}
=0
$