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5x^2+6x-15.75=0
a = 5; b = 6; c = -15.75;
Δ = b2-4ac
Δ = 62-4·5·(-15.75)
Δ = 351
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{351}=\sqrt{9*39}=\sqrt{9}*\sqrt{39}=3\sqrt{39}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-3\sqrt{39}}{2*5}=\frac{-6-3\sqrt{39}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+3\sqrt{39}}{2*5}=\frac{-6+3\sqrt{39}}{10} $
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