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-3n(8n-7)-6n=-219
We move all terms to the left:
-3n(8n-7)-6n-(-219)=0
We add all the numbers together, and all the variables
-6n-3n(8n-7)+219=0
We multiply parentheses
-24n^2-6n+21n+219=0
We add all the numbers together, and all the variables
-24n^2+15n+219=0
a = -24; b = 15; c = +219;
Δ = b2-4ac
Δ = 152-4·(-24)·219
Δ = 21249
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{21249}=\sqrt{9*2361}=\sqrt{9}*\sqrt{2361}=3\sqrt{2361}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{2361}}{2*-24}=\frac{-15-3\sqrt{2361}}{-48} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{2361}}{2*-24}=\frac{-15+3\sqrt{2361}}{-48} $
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