7/x+8/(x-2)=46

Solution for 7/x+8/(x-2)=46 equation:

7/x+8/(x-2)=46

We move all terms to the left:

7/x+8/(x-2)-(46)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: (x-2)!=0

We move all terms containing x to the left, all other terms to the right

x!=2

x∈R


We calculate fractions


(7x-14)/(x^2-2x)+8x/(x^2-2x)-46=0

We multiply all the terms by the denominator


(7x-14)+8x-46*(x^2-2x)=0

We add all the numbers together, and all the variables

8x+(7x-14)-46*(x^2-2x)=0

We multiply parentheses

-46x^2+8x+(7x-14)+92x=0

We get rid of parentheses

-46x^2+8x+7x+92x-14=0

We add all the numbers together, and all the variables

-46x^2+107x-14=0

a = -46; b = 107; c = -14;
Δ = b2-4ac
Δ = 1072-4·(-46)·(-14)
Δ = 8873
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(107)-\sqrt{8873}}{2*-46}=\frac{-107-\sqrt{8873}}{-92}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(107)+\sqrt{8873}}{2*-46}=\frac{-107+\sqrt{8873}}{-92}
$