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75x^2+45x-28=0
a = 75; b = 45; c = -28;
Δ = b2-4ac
Δ = 452-4·75·(-28)
Δ = 10425
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10425}=\sqrt{25*417}=\sqrt{25}*\sqrt{417}=5\sqrt{417}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-5\sqrt{417}}{2*75}=\frac{-45-5\sqrt{417}}{150} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+5\sqrt{417}}{2*75}=\frac{-45+5\sqrt{417}}{150} $
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