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8x(3x+2)=448
We move all terms to the left:
8x(3x+2)-(448)=0
We multiply parentheses
24x^2+16x-448=0
a = 24; b = 16; c = -448;
Δ = b2-4ac
Δ = 162-4·24·(-448)
Δ = 43264
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{43264}=208$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-208}{2*24}=\frac{-224}{48} =-4+2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+208}{2*24}=\frac{192}{48} =4 $
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