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8n^2+3n=143
We move all terms to the left:
8n^2+3n-(143)=0
a = 8; b = 3; c = -143;
Δ = b2-4ac
Δ = 32-4·8·(-143)
Δ = 4585
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{-(3)-\sqrt{4585}}{2*8}=\frac{-3-\sqrt{4585}}{16} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{4585}}{2*8}=\frac{-3+\sqrt{4585}}{16} $
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