-1/2x=6x+11

Solution for -1/2x=6x+11 equation:

-1/2x=6x+11

We move all terms to the left:

-1/2x-(6x+11)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

-1/2x-6x-11=0

We multiply all the terms by the denominator


-6x*2x-11*2x-1=0

Wy multiply elements

-12x^2-22x-1=0

a = -12; b = -22; c = -1;
Δ = b2-4ac
Δ = -222-4·(-12)·(-1)
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{109}}{2*-12}=\frac{22-2\sqrt{109}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{109}}{2*-12}=\frac{22+2\sqrt{109}}{-24}
$