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15x^2+46x+21=0
a = 15; b = 46; c = +21;
Δ = b2-4ac
Δ = 462-4·15·21
Δ = 856
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{856}=\sqrt{4*214}=\sqrt{4}*\sqrt{214}=2\sqrt{214}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{214}}{2*15}=\frac{-46-2\sqrt{214}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{214}}{2*15}=\frac{-46+2\sqrt{214}}{30} $
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