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8x(3+2x)+4x=384
We move all terms to the left:
8x(3+2x)+4x-(384)=0
We add all the numbers together, and all the variables
8x(2x+3)+4x-384=0
We add all the numbers together, and all the variables
4x+8x(2x+3)-384=0
We multiply parentheses
16x^2+4x+24x-384=0
We add all the numbers together, and all the variables
16x^2+28x-384=0
a = 16; b = 28; c = -384;
Δ = b2-4ac
Δ = 282-4·16·(-384)
Δ = 25360
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{25360}=\sqrt{16*1585}=\sqrt{16}*\sqrt{1585}=4\sqrt{1585}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{1585}}{2*16}=\frac{-28-4\sqrt{1585}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{1585}}{2*16}=\frac{-28+4\sqrt{1585}}{32} $
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