2g+5=1/2g+11

Solution for 2g+5=1/2g+11 equation:

2g+5=1/2g+11

We move all terms to the left:

2g+5-(1/2g+11)=0


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

g∈R


We get rid of parentheses

2g-1/2g-11+5=0

We multiply all the terms by the denominator


2g*2g-11*2g+5*2g-1=0

Wy multiply elements

4g^2-22g+10g-1=0

We add all the numbers together, and all the variables

4g^2-12g-1=0

a = 4; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·4·(-1)
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{10}}{2*4}=\frac{12-4\sqrt{10}}{8}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{10}}{2*4}=\frac{12+4\sqrt{10}}{8}
$