5n^2=41n-42

Solution for 5n^2=41n-42 equation:

5n^2=41n-42

We move all terms to the left:

5n^2-(41n-42)=0

We get rid of parentheses

5n^2-41n+42=0

a = 5; b = -41; c = +42;
Δ = b2-4ac
Δ = -412-4·5·42
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-29}{2*5}=\frac{12}{10}
=1+1/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+29}{2*5}=\frac{70}{10}
=7
$