-x-2=1/7x-10

Solution for -x-2=1/7x-10 equation:

-x-2=1/7x-10

We move all terms to the left:

-x-2-(1/7x-10)=0


Domain of the equation: 7x-10)!=0

x∈R


We add all the numbers together, and all the variables

-1x-(1/7x-10)-2=0

We get rid of parentheses

-1x-1/7x+10-2=0

We multiply all the terms by the denominator


-1x*7x+10*7x-2*7x-1=0

Wy multiply elements

-7x^2+70x-14x-1=0

We add all the numbers together, and all the variables

-7x^2+56x-1=0

a = -7; b = 56; c = -1;
Δ = b2-4ac
Δ = 562-4·(-7)·(-1)
Δ = 3108
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:

$\sqrt{\Delta}=\sqrt{3108}=\sqrt{4*777}=\sqrt{4}*\sqrt{777}=2\sqrt{777}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-2\sqrt{777}}{2*-7}=\frac{-56-2\sqrt{777}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+2\sqrt{777}}{2*-7}=\frac{-56+2\sqrt{777}}{-14}
$