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6x^2+30x-8=0
a = 6; b = 30; c = -8;
Δ = b2-4ac
Δ = 302-4·6·(-8)
Δ = 1092
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1092}=\sqrt{4*273}=\sqrt{4}*\sqrt{273}=2\sqrt{273}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{273}}{2*6}=\frac{-30-2\sqrt{273}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{273}}{2*6}=\frac{-30+2\sqrt{273}}{12} $
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