3/4g-9=4g+4

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

3/4g-9=4g+4

We move all terms to the left:

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


Domain of the equation: 4g!=0

g!=0/4

g!=0

g∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-16g^2-16g-36g+3=0

We add all the numbers together, and all the variables

-16g^2-52g+3=0

a = -16; b = -52; c = +3;
Δ = b2-4ac
Δ = -522-4·(-16)·3
Δ = 2896
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:

$\sqrt{\Delta}=\sqrt{2896}=\sqrt{16*181}=\sqrt{16}*\sqrt{181}=4\sqrt{181}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-4\sqrt{181}}{2*-16}=\frac{52-4\sqrt{181}}{-32}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+4\sqrt{181}}{2*-16}=\frac{52+4\sqrt{181}}{-32}
$