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5x^2=17
We move all terms to the left:
5x^2-(17)=0
a = 5; b = 0; c = -17;
Δ = b2-4ac
Δ = 02-4·5·(-17)
Δ = 340
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{85}}{2*5}=\frac{0-2\sqrt{85}}{10} =-\frac{2\sqrt{85}}{10} =-\frac{\sqrt{85}}{5} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{85}}{2*5}=\frac{0+2\sqrt{85}}{10} =\frac{2\sqrt{85}}{10} =\frac{\sqrt{85}}{5} $
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