3n+-40=1/2n+35

Solution for 3n+-40=1/2n+35 equation:

3n+-40=1/2n+35

We move all terms to the left:

3n+-40-(1/2n+35)=0


Domain of the equation: 2n+35)!=0

n∈R


We add all the numbers together, and all the variables

3n-(1/2n+35)=0

We get rid of parentheses

3n-1/2n-35=0

We multiply all the terms by the denominator


3n*2n-35*2n-1=0

Wy multiply elements

6n^2-70n-1=0

a = 6; b = -70; c = -1;
Δ = b2-4ac
Δ = -702-4·6·(-1)
Δ = 4924
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4924}=\sqrt{4*1231}=\sqrt{4}*\sqrt{1231}=2\sqrt{1231}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1231}}{2*6}=\frac{70-2\sqrt{1231}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1231}}{2*6}=\frac{70+2\sqrt{1231}}{12}
$