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6x^2-30x-74=0
a = 6; b = -30; c = -74;
Δ = b2-4ac
Δ = -302-4·6·(-74)
Δ = 2676
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2676}=\sqrt{4*669}=\sqrt{4}*\sqrt{669}=2\sqrt{669}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{669}}{2*6}=\frac{30-2\sqrt{669}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{669}}{2*6}=\frac{30+2\sqrt{669}}{12} $
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