7g-10=5+5/3g

Solution for 7g-10=5+5/3g equation:

7g-10=5+5/3g

We move all terms to the left:

7g-10-(5+5/3g)=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-(5/3g+5)-10=0

We get rid of parentheses

7g-5/3g-5-10=0

We multiply all the terms by the denominator


7g*3g-5*3g-10*3g-5=0

Wy multiply elements

21g^2-15g-30g-5=0

We add all the numbers together, and all the variables

21g^2-45g-5=0

a = 21; b = -45; c = -5;
Δ = b2-4ac
Δ = -452-4·21·(-5)
Δ = 2445
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{2445}}{2*21}=\frac{45-\sqrt{2445}}{42}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2445}}{2*21}=\frac{45+\sqrt{2445}}{42}
$