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6x^2-96x-134=0
a = 6; b = -96; c = -134;
Δ = b2-4ac
Δ = -962-4·6·(-134)
Δ = 12432
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{12432}=\sqrt{16*777}=\sqrt{16}*\sqrt{777}=4\sqrt{777}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-4\sqrt{777}}{2*6}=\frac{96-4\sqrt{777}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+4\sqrt{777}}{2*6}=\frac{96+4\sqrt{777}}{12} $
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