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4x^2=684
We move all terms to the left:
4x^2-(684)=0
a = 4; b = 0; c = -684;
Δ = b2-4ac
Δ = 02-4·4·(-684)
Δ = 10944
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10944}=\sqrt{576*19}=\sqrt{576}*\sqrt{19}=24\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{19}}{2*4}=\frac{0-24\sqrt{19}}{8} =-\frac{24\sqrt{19}}{8} =-3\sqrt{19} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{19}}{2*4}=\frac{0+24\sqrt{19}}{8} =\frac{24\sqrt{19}}{8} =3\sqrt{19} $
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