4n^2-26n=-30

Solution for 4n^2-26n=-30 equation:

4n^2-26n=-30

We move all terms to the left:

4n^2-26n-(-30)=0

We add all the numbers together, and all the variables

4n^2-26n+30=0

a = 4; b = -26; c = +30;
Δ = b2-4ac
Δ = -262-4·4·30
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-14}{2*4}=\frac{12}{8}
=1+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+14}{2*4}=\frac{40}{8}
=5
$