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75x^2+200x=10000
We move all terms to the left:
75x^2+200x-(10000)=0
a = 75; b = 200; c = -10000;
Δ = b2-4ac
Δ = 2002-4·75·(-10000)
Δ = 3040000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3040000}=\sqrt{160000*19}=\sqrt{160000}*\sqrt{19}=400\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-400\sqrt{19}}{2*75}=\frac{-200-400\sqrt{19}}{150} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+400\sqrt{19}}{2*75}=\frac{-200+400\sqrt{19}}{150} $
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