8/4g=g+9

Solution for 8/4g=g+9 equation:

8/4g=g+9

We move all terms to the left:

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


Domain of the equation: 4g!=0

g!=0/4

g!=0

g∈R


We get rid of parentheses

8/4g-g-9=0

We multiply all the terms by the denominator


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

Wy multiply elements

-4g^2-36g+8=0

a = -4; b = -36; c = +8;
Δ = b2-4ac
Δ = -362-4·(-4)·8
Δ = 1424
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:

$\sqrt{\Delta}=\sqrt{1424}=\sqrt{16*89}=\sqrt{16}*\sqrt{89}=4\sqrt{89}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{89}}{2*-4}=\frac{36-4\sqrt{89}}{-8}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{89}}{2*-4}=\frac{36+4\sqrt{89}}{-8}
$