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6x^2+58x-38=0
a = 6; b = 58; c = -38;
Δ = b2-4ac
Δ = 582-4·6·(-38)
Δ = 4276
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4276}=\sqrt{4*1069}=\sqrt{4}*\sqrt{1069}=2\sqrt{1069}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-2\sqrt{1069}}{2*6}=\frac{-58-2\sqrt{1069}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+2\sqrt{1069}}{2*6}=\frac{-58+2\sqrt{1069}}{12} $
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