g2=16/15

Solution for g2=16/15 equation:

g2=16/15

We move all terms to the left:

g2-(16/15)=0

We add all the numbers together, and all the variables

g2-(+16/15)=0

We add all the numbers together, and all the variables

g^2-(+16/15)=0

We get rid of parentheses

g^2-16/15=0

We multiply all the terms by the denominator


g^2*15-16=0

Wy multiply elements

15g^2-16=0

a = 15; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·15·(-16)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{15}}{2*15}=\frac{0-8\sqrt{15}}{30}
=-\frac{8\sqrt{15}}{30}
=-\frac{4\sqrt{15}}{15}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{15}}{2*15}=\frac{0+8\sqrt{15}}{30}
=\frac{8\sqrt{15}}{30}
=\frac{4\sqrt{15}}{15}
$