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21+15x-3x^2=0
a = -3; b = 15; c = +21;
Δ = b2-4ac
Δ = 152-4·(-3)·21
Δ = 477
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{477}=\sqrt{9*53}=\sqrt{9}*\sqrt{53}=3\sqrt{53}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{53}}{2*-3}=\frac{-15-3\sqrt{53}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{53}}{2*-3}=\frac{-15+3\sqrt{53}}{-6} $
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