5/3g=83g=

Solution for 5/3g=83g= equation:

5/3g=83g=

We move all terms to the left:

5/3g-(83g)=0


Domain of the equation: 3g!=0

g!=0/3

g!=0

g∈R


We add all the numbers together, and all the variables

-83g+5/3g=0

We multiply all the terms by the denominator


-83g*3g+5=0

Wy multiply elements

-249g^2+5=0

a = -249; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-249)·5
Δ = 4980
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:

$\sqrt{\Delta}=\sqrt{4980}=\sqrt{4*1245}=\sqrt{4}*\sqrt{1245}=2\sqrt{1245}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1245}}{2*-249}=\frac{0-2\sqrt{1245}}{-498}
=-\frac{2\sqrt{1245}}{-498}
=-\frac{\sqrt{1245}}{-249}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1245}}{2*-249}=\frac{0+2\sqrt{1245}}{-498}
=\frac{2\sqrt{1245}}{-498}
=\frac{\sqrt{1245}}{-249}
$