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15x^2+51x-45=0
a = 15; b = 51; c = -45;
Δ = b2-4ac
Δ = 512-4·15·(-45)
Δ = 5301
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5301}=\sqrt{9*589}=\sqrt{9}*\sqrt{589}=3\sqrt{589}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-3\sqrt{589}}{2*15}=\frac{-51-3\sqrt{589}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+3\sqrt{589}}{2*15}=\frac{-51+3\sqrt{589}}{30} $
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