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6(8n-5)(n-4)=0
We multiply parentheses ..
6(+8n^2-32n-5n+20)=0
We multiply parentheses
48n^2-192n-30n+120=0
We add all the numbers together, and all the variables
48n^2-222n+120=0
a = 48; b = -222; c = +120;
Δ = b2-4ac
Δ = -2222-4·48·120
Δ = 26244
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{26244}=162$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-222)-162}{2*48}=\frac{60}{96} =5/8 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-222)+162}{2*48}=\frac{384}{96} =4 $
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