1/2x-11=2x+3

Solution for 1/2x-11=2x+3 equation:

1/2x-11=2x+3

We move all terms to the left:

1/2x-11-(2x+3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-2x-3-11=0

We multiply all the terms by the denominator


-2x*2x-3*2x-11*2x+1=0

Wy multiply elements

-4x^2-6x-22x+1=0

We add all the numbers together, and all the variables

-4x^2-28x+1=0

a = -4; b = -28; c = +1;
Δ = b2-4ac
Δ = -282-4·(-4)·1
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-20\sqrt{2}}{2*-4}=\frac{28-20\sqrt{2}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+20\sqrt{2}}{2*-4}=\frac{28+20\sqrt{2}}{-8}
$