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

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

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

We move all terms to the left:

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


Domain of the equation: 2x+6)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2+12x+22x+1=0

We add all the numbers together, and all the variables

-4x^2+34x+1=0

a = -4; b = 34; c = +1;
Δ = b2-4ac
Δ = 342-4·(-4)·1
Δ = 1172
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:

$\sqrt{\Delta}=\sqrt{1172}=\sqrt{4*293}=\sqrt{4}*\sqrt{293}=2\sqrt{293}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{293}}{2*-4}=\frac{-34-2\sqrt{293}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{293}}{2*-4}=\frac{-34+2\sqrt{293}}{-8}
$