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

Solution for -1x+7/(x-2)=0 equation:

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


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 multiply all the terms by the denominator


-1x*(x-2)+7=0

We multiply parentheses

-x^2+2x+7=0

We add all the numbers together, and all the variables

-1x^2+2x+7=0

a = -1; b = 2; c = +7;
Δ = b2-4ac
Δ = 22-4·(-1)·7
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{2}}{2*-1}=\frac{-2-4\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{2}}{2*-1}=\frac{-2+4\sqrt{2}}{-2}
$