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3+5n=1+8n^2
We move all terms to the left:
3+5n-(1+8n^2)=0
We get rid of parentheses
-8n^2+5n-1+3=0
We add all the numbers together, and all the variables
-8n^2+5n+2=0
a = -8; b = 5; c = +2;
Δ = b2-4ac
Δ = 52-4·(-8)·2
Δ = 89
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{-(5)-\sqrt{89}}{2*-8}=\frac{-5-\sqrt{89}}{-16} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{89}}{2*-8}=\frac{-5+\sqrt{89}}{-16} $
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