(82/5)g=78

Solution for (82/5)g=78 equation:

(82/5)g=78

We move all terms to the left:

(82/5)g-(78)=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

(+82/5)g-78=0

We multiply parentheses

82g^2-78=0

a = 82; b = 0; c = -78;
Δ = b2-4ac
Δ = 02-4·82·(-78)
Δ = 25584
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:

$\sqrt{\Delta}=\sqrt{25584}=\sqrt{16*1599}=\sqrt{16}*\sqrt{1599}=4\sqrt{1599}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{1599}}{2*82}=\frac{0-4\sqrt{1599}}{164}
=-\frac{4\sqrt{1599}}{164}
=-\frac{\sqrt{1599}}{41}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{1599}}{2*82}=\frac{0+4\sqrt{1599}}{164}
=\frac{4\sqrt{1599}}{164}
=\frac{\sqrt{1599}}{41}
$