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9x^2+42x-7=0
a = 9; b = 42; c = -7;
Δ = b2-4ac
Δ = 422-4·9·(-7)
Δ = 2016
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2016}=\sqrt{144*14}=\sqrt{144}*\sqrt{14}=12\sqrt{14}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-12\sqrt{14}}{2*9}=\frac{-42-12\sqrt{14}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+12\sqrt{14}}{2*9}=\frac{-42+12\sqrt{14}}{18} $
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