7g-12=3+7/3g

Solution for 7g-12=3+7/3g equation:

7g-12=3+7/3g

We move all terms to the left:

7g-12-(3+7/3g)=0


Domain of the equation: 3g)!=0

g!=0/1

g!=0

g∈R


We add all the numbers together, and all the variables

7g-(7/3g+3)-12=0

We get rid of parentheses

7g-7/3g-3-12=0

We multiply all the terms by the denominator


7g*3g-3*3g-12*3g-7=0

Wy multiply elements

21g^2-9g-36g-7=0

We add all the numbers together, and all the variables

21g^2-45g-7=0

a = 21; b = -45; c = -7;
Δ = b2-4ac
Δ = -452-4·21·(-7)
Δ = 2613
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{2613}}{2*21}=\frac{45-\sqrt{2613}}{42}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2613}}{2*21}=\frac{45+\sqrt{2613}}{42}
$