3/4g-9=8g

Solution for 3/4g-9=8g equation:

3/4g-9=8g

We move all terms to the left:

3/4g-9-(8g)=0


Domain of the equation: 4g!=0

g!=0/4

g!=0

g∈R


We add all the numbers together, and all the variables

-8g+3/4g-9=0

We multiply all the terms by the denominator


-8g*4g-9*4g+3=0

Wy multiply elements

-32g^2-36g+3=0

a = -32; b = -36; c = +3;
Δ = b2-4ac
Δ = -362-4·(-32)·3
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{105}}{2*-32}=\frac{36-4\sqrt{105}}{-64}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{105}}{2*-32}=\frac{36+4\sqrt{105}}{-64}
$