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9x^2-68x-84=0
a = 9; b = -68; c = -84;
Δ = b2-4ac
Δ = -682-4·9·(-84)
Δ = 7648
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7648}=\sqrt{16*478}=\sqrt{16}*\sqrt{478}=4\sqrt{478}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-4\sqrt{478}}{2*9}=\frac{68-4\sqrt{478}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+4\sqrt{478}}{2*9}=\frac{68+4\sqrt{478}}{18} $
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