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8(n+2)(n+4)=1.144
We move all terms to the left:
8(n+2)(n+4)-(1.144)=0
We add all the numbers together, and all the variables
8(n+2)(n+4)-1.144=0
We multiply parentheses ..
8(+n^2+4n+2n+8)-1.144=0
We multiply parentheses
8n^2+32n+16n+64-1.144=0
We add all the numbers together, and all the variables
8n^2+48n+62.856=0
a = 8; b = 48; c = +62.856;
Δ = b2-4ac
Δ = 482-4·8·62.856
Δ = 292.608
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{-(48)-\sqrt{292.608}}{2*8}=\frac{-48-\sqrt{292.608}}{16} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+\sqrt{292.608}}{2*8}=\frac{-48+\sqrt{292.608}}{16} $
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