2/3g=45g=

Solution for 2/3g=45g= equation:

2/3g=45g=

We move all terms to the left:

2/3g-(45g)=0


Domain of the equation: 3g!=0

g!=0/3

g!=0

g∈R


We add all the numbers together, and all the variables

-45g+2/3g=0

We multiply all the terms by the denominator


-45g*3g+2=0

Wy multiply elements

-135g^2+2=0

a = -135; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-135)·2
Δ = 1080
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:

$\sqrt{\Delta}=\sqrt{1080}=\sqrt{36*30}=\sqrt{36}*\sqrt{30}=6\sqrt{30}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{30}}{2*-135}=\frac{0-6\sqrt{30}}{-270}
=-\frac{6\sqrt{30}}{-270}
=-\frac{\sqrt{30}}{-45}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{30}}{2*-135}=\frac{0+6\sqrt{30}}{-270}
=\frac{6\sqrt{30}}{-270}
=\frac{\sqrt{30}}{-45}
$