-7/x-1=14/5x+2

Solution for -7/x-1=14/5x+2 equation:

-7/x-1=14/5x+2

We move all terms to the left:

-7/x-1-(14/5x+2)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x+2)!=0

x∈R


We get rid of parentheses

-7/x-14/5x-2-1=0

We calculate fractions


(-35x)/5x^2+(-14x)/5x^2-2-1=0

We add all the numbers together, and all the variables

(-35x)/5x^2+(-14x)/5x^2-3=0

We multiply all the terms by the denominator


(-35x)+(-14x)-3*5x^2=0

Wy multiply elements

-15x^2+(-35x)+(-14x)=0

We get rid of parentheses

-15x^2-35x-14x=0

We add all the numbers together, and all the variables

-15x^2-49x=0

a = -15; b = -49; c = 0;
Δ = b2-4ac
Δ = -492-4·(-15)·0
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-49}{2*-15}=\frac{0}{-30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+49}{2*-15}=\frac{98}{-30}
=-3+4/15
$