n+7=2/3n+10

Solution for n+7=2/3n+10 equation:

n+7=2/3n+10

We move all terms to the left:

n+7-(2/3n+10)=0


Domain of the equation: 3n+10)!=0

n∈R


We get rid of parentheses

n-2/3n-10+7=0

We multiply all the terms by the denominator


n*3n-10*3n+7*3n-2=0

Wy multiply elements

3n^2-30n+21n-2=0

We add all the numbers together, and all the variables

3n^2-9n-2=0

a = 3; b = -9; c = -2;
Δ = b2-4ac
Δ = -92-4·3·(-2)
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{105}}{2*3}=\frac{9-\sqrt{105}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{105}}{2*3}=\frac{9+\sqrt{105}}{6}
$