-57-11/2x=-3x-2

Solution for -57-11/2x=-3x-2 equation:

-57-11/2x=-3x-2

We move all terms to the left:

-57-11/2x-(-3x-2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

-11/2x+3x+2-57=0

We multiply all the terms by the denominator


3x*2x+2*2x-57*2x-11=0

Wy multiply elements

6x^2+4x-114x-11=0

We add all the numbers together, and all the variables

6x^2-110x-11=0

a = 6; b = -110; c = -11;
Δ = b2-4ac
Δ = -1102-4·6·(-11)
Δ = 12364
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:

$\sqrt{\Delta}=\sqrt{12364}=\sqrt{4*3091}=\sqrt{4}*\sqrt{3091}=2\sqrt{3091}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-2\sqrt{3091}}{2*6}=\frac{110-2\sqrt{3091}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+2\sqrt{3091}}{2*6}=\frac{110+2\sqrt{3091}}{12}
$