(82/6)g=66

Solution for (82/6)g=66 equation:

(82/6)g=66

We move all terms to the left:

(82/6)g-(66)=0


Domain of the equation: 6)g!=0

g!=0/1

g!=0

g∈R


We add all the numbers together, and all the variables

(+82/6)g-66=0

We multiply parentheses

82g^2-66=0

a = 82; b = 0; c = -66;
Δ = b2-4ac
Δ = 02-4·82·(-66)
Δ = 21648
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:

$\sqrt{\Delta}=\sqrt{21648}=\sqrt{16*1353}=\sqrt{16}*\sqrt{1353}=4\sqrt{1353}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{1353}}{2*82}=\frac{0-4\sqrt{1353}}{164}
=-\frac{4\sqrt{1353}}{164}
=-\frac{\sqrt{1353}}{41}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{1353}}{2*82}=\frac{0+4\sqrt{1353}}{164}
=\frac{4\sqrt{1353}}{164}
=\frac{\sqrt{1353}}{41}
$