2n^2-7n=24

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

2n^2-7n=24

We move all terms to the left:

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

a = 2; b = -7; c = -24;
Δ = b2-4ac
Δ = -72-4·2·(-24)
Δ = 241
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{-(-7)-\sqrt{241}}{2*2}=\frac{7-\sqrt{241}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{241}}{2*2}=\frac{7+\sqrt{241}}{4}
$