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21y^2-3y-42=0
a = 21; b = -3; c = -42;
Δ = b2-4ac
Δ = -32-4·21·(-42)
Δ = 3537
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3537}=\sqrt{9*393}=\sqrt{9}*\sqrt{393}=3\sqrt{393}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{393}}{2*21}=\frac{3-3\sqrt{393}}{42} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{393}}{2*21}=\frac{3+3\sqrt{393}}{42} $
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