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12v^2-12v-22=0
a = 12; b = -12; c = -22;
Δ = b2-4ac
Δ = -122-4·12·(-22)
Δ = 1200
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}$$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-20\sqrt{3}}{2*12}=\frac{12-20\sqrt{3}}{24} $$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+20\sqrt{3}}{2*12}=\frac{12+20\sqrt{3}}{24} $
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