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12n(n+3)=11n-12
We move all terms to the left:
12n(n+3)-(11n-12)=0
We multiply parentheses
12n^2+36n-(11n-12)=0
We get rid of parentheses
12n^2+36n-11n+12=0
We add all the numbers together, and all the variables
12n^2+25n+12=0
a = 12; b = 25; c = +12;
Δ = b2-4ac
Δ = 252-4·12·12
Δ = 49
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{49}=7$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-7}{2*12}=\frac{-32}{24} =-1+1/3 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+7}{2*12}=\frac{-18}{24} =-3/4 $
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