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16x(8+24x)=320
We move all terms to the left:
16x(8+24x)-(320)=0
We add all the numbers together, and all the variables
16x(24x+8)-320=0
We multiply parentheses
384x^2+128x-320=0
a = 384; b = 128; c = -320;
Δ = b2-4ac
Δ = 1282-4·384·(-320)
Δ = 507904
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{507904}=\sqrt{16384*31}=\sqrt{16384}*\sqrt{31}=128\sqrt{31}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-128\sqrt{31}}{2*384}=\frac{-128-128\sqrt{31}}{768} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+128\sqrt{31}}{2*384}=\frac{-128+128\sqrt{31}}{768} $
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