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5n^2-3n-378=0
a = 5; b = -3; c = -378;
Δ = b2-4ac
Δ = -32-4·5·(-378)
Δ = 7569
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{7569}=87$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-87}{2*5}=\frac{-84}{10} =-8+2/5 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+87}{2*5}=\frac{90}{10} =9 $
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