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9x^2-84x-137=0
a = 9; b = -84; c = -137;
Δ = b2-4ac
Δ = -842-4·9·(-137)
Δ = 11988
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{11988}=\sqrt{324*37}=\sqrt{324}*\sqrt{37}=18\sqrt{37}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-18\sqrt{37}}{2*9}=\frac{84-18\sqrt{37}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+18\sqrt{37}}{2*9}=\frac{84+18\sqrt{37}}{18} $
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