3/4g-9=4g+1

Solution for 3/4g-9=4g+1 equation:

3/4g-9=4g+1

We move all terms to the left:

3/4g-9-(4g+1)=0


Domain of the equation: 4g!=0

g!=0/4

g!=0

g∈R


We get rid of parentheses

3/4g-4g-1-9=0

We multiply all the terms by the denominator


-4g*4g-1*4g-9*4g+3=0

Wy multiply elements

-16g^2-4g-36g+3=0

We add all the numbers together, and all the variables

-16g^2-40g+3=0

a = -16; b = -40; c = +3;
Δ = b2-4ac
Δ = -402-4·(-16)·3
Δ = 1792
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:

$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-16\sqrt{7}}{2*-16}=\frac{40-16\sqrt{7}}{-32}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+16\sqrt{7}}{2*-16}=\frac{40+16\sqrt{7}}{-32}
$