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21x^2-177x+67=0
a = 21; b = -177; c = +67;
Δ = b2-4ac
Δ = -1772-4·21·67
Δ = 25701
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{-(-177)-\sqrt{25701}}{2*21}=\frac{177-\sqrt{25701}}{42} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-177)+\sqrt{25701}}{2*21}=\frac{177+\sqrt{25701}}{42} $
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