5/8g+45/4=1/6g+3

Solution for 5/8g+45/4=1/6g+3 equation:

5/8g+45/4=1/6g+3

We move all terms to the left:

5/8g+45/4-(1/6g+3)=0


Domain of the equation: 8g!=0

g!=0/8

g!=0

g∈R



Domain of the equation: 6g+3)!=0

g∈R


We get rid of parentheses

5/8g-1/6g-3+45/4=0

We calculate fractions


12960g^2/768g^2+480g/768g^2+(-128g)/768g^2-3=0

We multiply all the terms by the denominator


12960g^2+480g+(-128g)-3*768g^2=0

Wy multiply elements

12960g^2-2304g^2+480g+(-128g)=0

We get rid of parentheses

12960g^2-2304g^2+480g-128g=0

We add all the numbers together, and all the variables

10656g^2+352g=0

a = 10656; b = 352; c = 0;
Δ = b2-4ac
Δ = 3522-4·10656·0
Δ = 123904
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{123904}=352$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(352)-352}{2*10656}=\frac{-704}{21312}
=-11/333
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(352)+352}{2*10656}=\frac{0}{21312}
=0
$