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x(x+75)=375
We move all terms to the left:
x(x+75)-(375)=0
We multiply parentheses
x^2+75x-375=0
a = 1; b = 75; c = -375;
Δ = b2-4ac
Δ = 752-4·1·(-375)
Δ = 7125
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7125}=\sqrt{25*285}=\sqrt{25}*\sqrt{285}=5\sqrt{285}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-5\sqrt{285}}{2*1}=\frac{-75-5\sqrt{285}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+5\sqrt{285}}{2*1}=\frac{-75+5\sqrt{285}}{2} $
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