(45n+60)+n(2/5)=-41

Solution for (45n+60)+n(2/5)=-41 equation:

(45n+60)+n(2/5)=-41

We move all terms to the left:

(45n+60)+n(2/5)-(-41)=0

We add all the numbers together, and all the variables

(45n+60)+n(+2/5)-(-41)=0

We add all the numbers together, and all the variables

(45n+60)+n(+2/5)+41=0

We multiply parentheses

2n^2+(45n+60)+41=0

We get rid of parentheses

2n^2+45n+60+41=0

We add all the numbers together, and all the variables

2n^2+45n+101=0

a = 2; b = 45; c = +101;
Δ = b2-4ac
Δ = 452-4·2·101
Δ = 1217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-\sqrt{1217}}{2*2}=\frac{-45-\sqrt{1217}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{1217}}{2*2}=\frac{-45+\sqrt{1217}}{4}
$