5n^2+14n=24

Solution for 5n^2+14n=24 equation:

5n^2+14n=24

We move all terms to the left:

5n^2+14n-(24)=0

a = 5; b = 14; c = -24;
Δ = b2-4ac
Δ = 142-4·5·(-24)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-26}{2*5}=\frac{-40}{10}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+26}{2*5}=\frac{12}{10}
=1+1/5
$