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3n(6n-1)=4n+67
We move all terms to the left:
3n(6n-1)-(4n+67)=0
We multiply parentheses
18n^2-3n-(4n+67)=0
We get rid of parentheses
18n^2-3n-4n-67=0
We add all the numbers together, and all the variables
18n^2-7n-67=0
a = 18; b = -7; c = -67;
Δ = b2-4ac
Δ = -72-4·18·(-67)
Δ = 4873
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{-(-7)-\sqrt{4873}}{2*18}=\frac{7-\sqrt{4873}}{36} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{4873}}{2*18}=\frac{7+\sqrt{4873}}{36} $
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