(44/5)g=4/5

Solution for (44/5)g=4/5 equation:

(44/5)g=4/5

We move all terms to the left:

(44/5)g-(4/5)=0


Domain of the equation: 5)g!=0

g!=0/1

g!=0

g∈R


We add all the numbers together, and all the variables

(+44/5)g-(+4/5)=0

We multiply parentheses

44g^2-(+4/5)=0

We get rid of parentheses

44g^2-4/5=0

We multiply all the terms by the denominator


44g^2*5-4=0

Wy multiply elements

220g^2-4=0

a = 220; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·220·(-4)
Δ = 3520
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:

$\sqrt{\Delta}=\sqrt{3520}=\sqrt{64*55}=\sqrt{64}*\sqrt{55}=8\sqrt{55}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{55}}{2*220}=\frac{0-8\sqrt{55}}{440}
=-\frac{8\sqrt{55}}{440}
=-\frac{\sqrt{55}}{55}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{55}}{2*220}=\frac{0+8\sqrt{55}}{440}
=\frac{8\sqrt{55}}{440}
=\frac{\sqrt{55}}{55}
$