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2a^2-21a-65=0
a = 2; b = -21; c = -65;
Δ = b2-4ac
Δ = -212-4·2·(-65)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{961}=31$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-31}{2*2}=\frac{-10}{4} =-2+1/2 $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+31}{2*2}=\frac{52}{4} =13 $
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