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4x^2-58x-8=0
a = 4; b = -58; c = -8;
Δ = b2-4ac
Δ = -582-4·4·(-8)
Δ = 3492
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3492}=\sqrt{36*97}=\sqrt{36}*\sqrt{97}=6\sqrt{97}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-6\sqrt{97}}{2*4}=\frac{58-6\sqrt{97}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+6\sqrt{97}}{2*4}=\frac{58+6\sqrt{97}}{8} $
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