30/g=g-7

Solution for 30/g=g-7 equation:

30/g=g-7

We move all terms to the left:

30/g-(g-7)=0


Domain of the equation: g!=0

g∈R


We get rid of parentheses

30/g-g+7=0

We multiply all the terms by the denominator


-g*g+7*g+30=0

We add all the numbers together, and all the variables

7g-g*g+30=0

Wy multiply elements

-1g^2+7g+30=0

a = -1; b = 7; c = +30;
Δ = b2-4ac
Δ = 72-4·(-1)·30
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-13}{2*-1}=\frac{-20}{-2}
=+10
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*-1}=\frac{6}{-2}
=-3
$