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2x(4x-16)=110
We move all terms to the left:
2x(4x-16)-(110)=0
We multiply parentheses
8x^2-32x-110=0
a = 8; b = -32; c = -110;
Δ = b2-4ac
Δ = -322-4·8·(-110)
Δ = 4544
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4544}=\sqrt{64*71}=\sqrt{64}*\sqrt{71}=8\sqrt{71}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{71}}{2*8}=\frac{32-8\sqrt{71}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{71}}{2*8}=\frac{32+8\sqrt{71}}{16} $
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