2g-2=8/2g-3

Solution for 2g-2=8/2g-3 equation:

2g-2=8/2g-3

We move all terms to the left:

2g-2-(8/2g-3)=0


Domain of the equation: 2g-3)!=0

g∈R


We get rid of parentheses

2g-8/2g+3-2=0

We multiply all the terms by the denominator


2g*2g+3*2g-2*2g-8=0

Wy multiply elements

4g^2+6g-4g-8=0

We add all the numbers together, and all the variables

4g^2+2g-8=0

a = 4; b = 2; c = -8;
Δ = b2-4ac
Δ = 22-4·4·(-8)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{33}}{2*4}=\frac{-2-2\sqrt{33}}{8}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{33}}{2*4}=\frac{-2+2\sqrt{33}}{8}
$