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8(5x^2)=64
We move all terms to the left:
8(5x^2)-(64)=0
a = 85; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·85·(-64)
Δ = 21760
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{21760}=\sqrt{256*85}=\sqrt{256}*\sqrt{85}=16\sqrt{85}x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{85}}{2*85}=\frac{0-16\sqrt{85}}{170} =-\frac{16\sqrt{85}}{170} =-\frac{8\sqrt{85}}{85}x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{85}}{2*85}=\frac{0+16\sqrt{85}}{170} =\frac{16\sqrt{85}}{170} =\frac{8\sqrt{85}}{85}
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