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75+80x-10.5x^2=0
a = -10.5; b = 80; c = +75;
Δ = b2-4ac
Δ = 802-4·(-10.5)·75
Δ = 9550
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9550}=\sqrt{25*382}=\sqrt{25}*\sqrt{382}=5\sqrt{382}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-5\sqrt{382}}{2*-10.5}=\frac{-80-5\sqrt{382}}{-21} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+5\sqrt{382}}{2*-10.5}=\frac{-80+5\sqrt{382}}{-21} $
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