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6y^2+14y-69=0
a = 6; b = 14; c = -69;
Δ = b2-4ac
Δ = 142-4·6·(-69)
Δ = 1852
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1852}=\sqrt{4*463}=\sqrt{4}*\sqrt{463}=2\sqrt{463}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{463}}{2*6}=\frac{-14-2\sqrt{463}}{12} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{463}}{2*6}=\frac{-14+2\sqrt{463}}{12} $
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