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32x^2-16=64
We move all terms to the left:
32x^2-16-(64)=0
We add all the numbers together, and all the variables
32x^2-80=0
a = 32; b = 0; c = -80;
Δ = b2-4ac
Δ = 02-4·32·(-80)
Δ = 10240
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10240}=\sqrt{1024*10}=\sqrt{1024}*\sqrt{10}=32\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{10}}{2*32}=\frac{0-32\sqrt{10}}{64} =-\frac{32\sqrt{10}}{64} =-\frac{\sqrt{10}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{10}}{2*32}=\frac{0+32\sqrt{10}}{64} =\frac{32\sqrt{10}}{64} =\frac{\sqrt{10}}{2} $
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