2/g+6=4/5g+10

Solution for 2/g+6=4/5g+10 equation:

2/g+6=4/5g+10

We move all terms to the left:

2/g+6-(4/5g+10)=0


Domain of the equation: g!=0

g∈R



Domain of the equation: 5g+10)!=0

g∈R


We get rid of parentheses

2/g-4/5g-10+6=0

We calculate fractions


10g/5g^2+(-4g)/5g^2-10+6=0

We add all the numbers together, and all the variables

10g/5g^2+(-4g)/5g^2-4=0

We multiply all the terms by the denominator


10g+(-4g)-4*5g^2=0

Wy multiply elements

-20g^2+10g+(-4g)=0

We get rid of parentheses

-20g^2+10g-4g=0

We add all the numbers together, and all the variables

-20g^2+6g=0

a = -20; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-20)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-20}=\frac{-12}{-40}
=3/10
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-20}=\frac{0}{-40}
=0
$