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9v^2-68v+21=0
a = 9; b = -68; c = +21;
Δ = b2-4ac
Δ = -682-4·9·21
Δ = 3868
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3868}=\sqrt{4*967}=\sqrt{4}*\sqrt{967}=2\sqrt{967}$$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-2\sqrt{967}}{2*9}=\frac{68-2\sqrt{967}}{18} $$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+2\sqrt{967}}{2*9}=\frac{68+2\sqrt{967}}{18} $
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