.25n+10=2/3n

Solution for .25n+10=2/3n equation:

.25n+10=2/3n

We move all terms to the left:

.25n+10-(2/3n)=0


Domain of the equation: 3n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

.25n-(+2/3n)+10=0

We get rid of parentheses

.25n-2/3n+10=0

We multiply all the terms by the denominator


(.25n)*3n+10*3n-2=0

We add all the numbers together, and all the variables

(+.25n)*3n+10*3n-2=0

We multiply parentheses

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

Wy multiply elements

3n^2+30n-2=0

a = 3; b = 30; c = -2;
Δ = b2-4ac
Δ = 302-4·3·(-2)
Δ = 924
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:

$\sqrt{\Delta}=\sqrt{924}=\sqrt{4*231}=\sqrt{4}*\sqrt{231}=2\sqrt{231}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{231}}{2*3}=\frac{-30-2\sqrt{231}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{231}}{2*3}=\frac{-30+2\sqrt{231}}{6}
$