7/x-2+9/5x-10=-7

Solution for 7/x-2+9/5x-10=-7 equation:

7/x-2+9/5x-10=-7

We move all terms to the left:

7/x-2+9/5x-10-(-7)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

7/x+9/5x-5=0

We calculate fractions


35x/5x^2+9x/5x^2-5=0

We multiply all the terms by the denominator


35x+9x-5*5x^2=0

We add all the numbers together, and all the variables

44x-5*5x^2=0

Wy multiply elements

-25x^2+44x=0

a = -25; b = 44; c = 0;
Δ = b2-4ac
Δ = 442-4·(-25)·0
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-44}{2*-25}=\frac{-88}{-50}
=1+19/25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+44}{2*-25}=\frac{0}{-50}
=0
$