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(2n+11)(3n+7)=0
We multiply parentheses ..
(+6n^2+14n+33n+77)=0
We get rid of parentheses
6n^2+14n+33n+77=0
We add all the numbers together, and all the variables
6n^2+47n+77=0
a = 6; b = 47; c = +77;
Δ = b2-4ac
Δ = 472-4·6·77
Δ = 361
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{361}=19$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-19}{2*6}=\frac{-66}{12} =-5+1/2 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+19}{2*6}=\frac{-28}{12} =-2+1/3 $
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