n+8=3/4n+7

Solution for n+8=3/4n+7 equation:

n+8=3/4n+7

We move all terms to the left:

n+8-(3/4n+7)=0


Domain of the equation: 4n+7)!=0

n∈R


We get rid of parentheses

n-3/4n-7+8=0

We multiply all the terms by the denominator


n*4n-7*4n+8*4n-3=0

Wy multiply elements

4n^2-28n+32n-3=0

We add all the numbers together, and all the variables

4n^2+4n-3=0

a = 4; b = 4; c = -3;
Δ = b2-4ac
Δ = 42-4·4·(-3)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8}{2*4}=\frac{-12}{8}
=-1+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*4}=\frac{4}{8}
=1/2
$