3g-5=7/g=

Solution for 3g-5=7/g= equation:

3g-5=7/g=

We move all terms to the left:

3g-5-(7/g)=0


Domain of the equation: g)!=0

g!=0/1

g!=0

g∈R


We add all the numbers together, and all the variables

3g-(+7/g)-5=0

We get rid of parentheses

3g-7/g-5=0

We multiply all the terms by the denominator


3g*g-5*g-7=0

We add all the numbers together, and all the variables

-5g+3g*g-7=0

Wy multiply elements

3g^2-5g-7=0

a = 3; b = -5; c = -7;
Δ = b2-4ac
Δ = -52-4·3·(-7)
Δ = 109
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{-(-5)-\sqrt{109}}{2*3}=\frac{5-\sqrt{109}}{6}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{109}}{2*3}=\frac{5+\sqrt{109}}{6}
$