(x+35)/(x)-(x-2)/(3)=1

Solution for (x+35)/(x)-(x-2)/(3)=1 equation:

(x+35)/(x)-(x-2)/(3)=1

We move all terms to the left:

(x+35)/(x)-(x-2)/(3)-(1)=0


Domain of the equation: x!=0

x∈R


We calculate fractions


(-1x^2+2x)/3x+(3x+105)/3x-1=0

We multiply all the terms by the denominator


(-1x^2+2x)+(3x+105)-1*3x=0

Wy multiply elements

(-1x^2+2x)+(3x+105)-3x=0

We get rid of parentheses

-1x^2+2x+3x-3x+105=0

We add all the numbers together, and all the variables

-1x^2+2x+105=0

a = -1; b = 2; c = +105;
Δ = b2-4ac
Δ = 22-4·(-1)·105
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{106}}{2*-1}=\frac{-2-2\sqrt{106}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{106}}{2*-1}=\frac{-2+2\sqrt{106}}{-2}
$