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11x^2-34x-21=0
a = 11; b = -34; c = -21;
Δ = b2-4ac
Δ = -342-4·11·(-21)
Δ = 2080
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2080}=\sqrt{16*130}=\sqrt{16}*\sqrt{130}=4\sqrt{130}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-4\sqrt{130}}{2*11}=\frac{34-4\sqrt{130}}{22} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+4\sqrt{130}}{2*11}=\frac{34+4\sqrt{130}}{22} $
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