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21x^2-83x+34=0
a = 21; b = -83; c = +34;
Δ = b2-4ac
Δ = -832-4·21·34
Δ = 4033
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-83)-\sqrt{4033}}{2*21}=\frac{83-\sqrt{4033}}{42} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-83)+\sqrt{4033}}{2*21}=\frac{83+\sqrt{4033}}{42} $
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