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6x^2-17x-14/286=0
We multiply all the terms by the denominator
6x^2*286-17x*286-14=0
Wy multiply elements
1716x^2-4862x-14=0
a = 1716; b = -4862; c = -14;
Δ = b2-4ac
Δ = -48622-4·1716·(-14)
Δ = 23735140
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{23735140}=\sqrt{4*5933785}=\sqrt{4}*\sqrt{5933785}=2\sqrt{5933785}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4862)-2\sqrt{5933785}}{2*1716}=\frac{4862-2\sqrt{5933785}}{3432} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4862)+2\sqrt{5933785}}{2*1716}=\frac{4862+2\sqrt{5933785}}{3432} $
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