2/5g-3=-1/2g

Solution for 2/5g-3=-1/2g equation:

2/5g-3=-1/2g

We move all terms to the left:

2/5g-3-(-1/2g)=0


Domain of the equation: 5g!=0

g!=0/5

g!=0

g∈R



Domain of the equation: 2g)!=0

g!=0/1

g!=0

g∈R


We get rid of parentheses

2/5g+1/2g-3=0

We calculate fractions


4g/10g^2+5g/10g^2-3=0

We multiply all the terms by the denominator


4g+5g-3*10g^2=0

We add all the numbers together, and all the variables

9g-3*10g^2=0

Wy multiply elements

-30g^2+9g=0

a = -30; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-30)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-30}=\frac{-18}{-60}
=3/10
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-30}=\frac{0}{-60}
=0
$