-5/6n+8=3/4n-7

Solution for -5/6n+8=3/4n-7 equation:

-5/6n+8=3/4n-7

We move all terms to the left:

-5/6n+8-(3/4n-7)=0


Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R



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

n∈R


We get rid of parentheses

-5/6n-3/4n+7+8=0

We calculate fractions


(-20n)/24n^2+(-18n)/24n^2+7+8=0

We add all the numbers together, and all the variables

(-20n)/24n^2+(-18n)/24n^2+15=0

We multiply all the terms by the denominator


(-20n)+(-18n)+15*24n^2=0

Wy multiply elements

360n^2+(-20n)+(-18n)=0

We get rid of parentheses

360n^2-20n-18n=0

We add all the numbers together, and all the variables

360n^2-38n=0

a = 360; b = -38; c = 0;
Δ = b2-4ac
Δ = -382-4·360·0
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-38}{2*360}=\frac{0}{720}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+38}{2*360}=\frac{76}{720}
=19/180
$