5n^2-7n-12=0

Solution for 5n^2-7n-12=0 equation:

5n^2-7n-12=0

a = 5; b = -7; c = -12;
Δ = b2-4ac
Δ = -72-4·5·(-12)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-17}{2*5}=\frac{-10}{10}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+17}{2*5}=\frac{24}{10}
=2+2/5
$