-2x-7=11/7x+6

Solution for -2x-7=11/7x+6 equation:

-2x-7=11/7x+6

We move all terms to the left:

-2x-7-(11/7x+6)=0


Domain of the equation: 7x+6)!=0

x∈R


We get rid of parentheses

-2x-11/7x-6-7=0

We multiply all the terms by the denominator


-2x*7x-6*7x-7*7x-11=0

Wy multiply elements

-14x^2-42x-49x-11=0

We add all the numbers together, and all the variables

-14x^2-91x-11=0

a = -14; b = -91; c = -11;
Δ = b2-4ac
Δ = -912-4·(-14)·(-11)
Δ = 7665
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{-(-91)-\sqrt{7665}}{2*-14}=\frac{91-\sqrt{7665}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-91)+\sqrt{7665}}{2*-14}=\frac{91+\sqrt{7665}}{-28}
$