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6x(4x+1)=408
We move all terms to the left:
6x(4x+1)-(408)=0
We multiply parentheses
24x^2+6x-408=0
a = 24; b = 6; c = -408;
Δ = b2-4ac
Δ = 62-4·24·(-408)
Δ = 39204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{39204}=198$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-198}{2*24}=\frac{-204}{48} =-4+1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+198}{2*24}=\frac{192}{48} =4 $
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