35=x-3/x-7=4

Solution for 35=x-3/x-7=4 equation:

35=x-3/x-7=4

We move all terms to the left:

35-(x-3/x-7)=0


Domain of the equation: x-7)!=0

x∈R


We get rid of parentheses

-x+3/x+7+35=0

We multiply all the terms by the denominator


-x*x+7*x+35*x+3=0

We add all the numbers together, and all the variables

42x-x*x+3=0

Wy multiply elements

-1x^2+42x+3=0

a = -1; b = 42; c = +3;
Δ = b2-4ac
Δ = 422-4·(-1)·3
Δ = 1776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1776}=\sqrt{16*111}=\sqrt{16}*\sqrt{111}=4\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-4\sqrt{111}}{2*-1}=\frac{-42-4\sqrt{111}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+4\sqrt{111}}{2*-1}=\frac{-42+4\sqrt{111}}{-2}
$