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(8n+3)(3n-2)=0
We multiply parentheses ..
(+24n^2-16n+9n-6)=0
We get rid of parentheses
24n^2-16n+9n-6=0
We add all the numbers together, and all the variables
24n^2-7n-6=0
a = 24; b = -7; c = -6;
Δ = b2-4ac
Δ = -72-4·24·(-6)
Δ = 625
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{625}=25$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-25}{2*24}=\frac{-18}{48} =-3/8 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+25}{2*24}=\frac{32}{48} =2/3 $
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