3x+7=1/2x+11

Solution for 3x+7=1/2x+11 equation:

3x+7=1/2x+11

We move all terms to the left:

3x+7-(1/2x+11)=0


Domain of the equation: 2x+11)!=0

x∈R


We get rid of parentheses

3x-1/2x-11+7=0

We multiply all the terms by the denominator


3x*2x-11*2x+7*2x-1=0

Wy multiply elements

6x^2-22x+14x-1=0

We add all the numbers together, and all the variables

6x^2-8x-1=0

a = 6; b = -8; c = -1;
Δ = b2-4ac
Δ = -82-4·6·(-1)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{22}}{2*6}=\frac{8-2\sqrt{22}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{22}}{2*6}=\frac{8+2\sqrt{22}}{12}
$