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-2n(-6-7n)+5n=145
We move all terms to the left:
-2n(-6-7n)+5n-(145)=0
We add all the numbers together, and all the variables
-2n(-7n-6)+5n-145=0
We add all the numbers together, and all the variables
5n-2n(-7n-6)-145=0
We multiply parentheses
14n^2+5n+12n-145=0
We add all the numbers together, and all the variables
14n^2+17n-145=0
a = 14; b = 17; c = -145;
Δ = b2-4ac
Δ = 172-4·14·(-145)
Δ = 8409
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{-(17)-\sqrt{8409}}{2*14}=\frac{-17-\sqrt{8409}}{28} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{8409}}{2*14}=\frac{-17+\sqrt{8409}}{28} $
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