n^2+3n-7=24

Solution for n^2+3n-7=24 equation:

n^2+3n-7=24

We move all terms to the left:

n^2+3n-7-(24)=0

We add all the numbers together, and all the variables

n^2+3n-31=0

a = 1; b = 3; c = -31;
Δ = b2-4ac
Δ = 32-4·1·(-31)
Δ = 133
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{-(3)-\sqrt{133}}{2*1}=\frac{-3-\sqrt{133}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{133}}{2*1}=\frac{-3+\sqrt{133}}{2}
$