4/5*n=34

Solution for 4/5*n=34 equation:

4/5*n=34

We move all terms to the left:

4/5*n-(34)=0


Domain of the equation: 5*n!=0

n!=0/1

n!=0

n∈R


We multiply all the terms by the denominator


-34*5*n+4=0

Wy multiply elements

-170n*n+4=0

Wy multiply elements

-170n^2+4=0

a = -170; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-170)·4
Δ = 2720
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:

$\sqrt{\Delta}=\sqrt{2720}=\sqrt{16*170}=\sqrt{16}*\sqrt{170}=4\sqrt{170}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{170}}{2*-170}=\frac{0-4\sqrt{170}}{-340}
=-\frac{4\sqrt{170}}{-340}
=-\frac{\sqrt{170}}{-85}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{170}}{2*-170}=\frac{0+4\sqrt{170}}{-340}
=\frac{4\sqrt{170}}{-340}
=\frac{\sqrt{170}}{-85}
$