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5z^2+51z+45=0
a = 5; b = 51; c = +45;
Δ = b2-4ac
Δ = 512-4·5·45
Δ = 1701
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1701}=\sqrt{81*21}=\sqrt{81}*\sqrt{21}=9\sqrt{21}$$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-9\sqrt{21}}{2*5}=\frac{-51-9\sqrt{21}}{10} $$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+9\sqrt{21}}{2*5}=\frac{-51+9\sqrt{21}}{10} $
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