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15x^2-38x-84=0
a = 15; b = -38; c = -84;
Δ = b2-4ac
Δ = -382-4·15·(-84)
Δ = 6484
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6484}=\sqrt{4*1621}=\sqrt{4}*\sqrt{1621}=2\sqrt{1621}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{1621}}{2*15}=\frac{38-2\sqrt{1621}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{1621}}{2*15}=\frac{38+2\sqrt{1621}}{30} $
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