1/2n+10=2n-35

Solution for 1/2n+10=2n-35 equation:

1/2n+10=2n-35

We move all terms to the left:

1/2n+10-(2n-35)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We get rid of parentheses

1/2n-2n+35+10=0

We multiply all the terms by the denominator


-2n*2n+35*2n+10*2n+1=0

Wy multiply elements

-4n^2+70n+20n+1=0

We add all the numbers together, and all the variables

-4n^2+90n+1=0

a = -4; b = 90; c = +1;
Δ = b2-4ac
Δ = 902-4·(-4)·1
Δ = 8116
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:

$\sqrt{\Delta}=\sqrt{8116}=\sqrt{4*2029}=\sqrt{4}*\sqrt{2029}=2\sqrt{2029}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2029}}{2*-4}=\frac{-90-2\sqrt{2029}}{-8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2029}}{2*-4}=\frac{-90+2\sqrt{2029}}{-8}
$