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5x+100x*500x=400
We move all terms to the left:
5x+100x*500x-(400)=0
Wy multiply elements
50000x^2+5x-400=0
a = 50000; b = 5; c = -400;
Δ = b2-4ac
Δ = 52-4·50000·(-400)
Δ = 80000025
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{80000025}=\sqrt{25*3200001}=\sqrt{25}*\sqrt{3200001}=5\sqrt{3200001}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{3200001}}{2*50000}=\frac{-5-5\sqrt{3200001}}{100000} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{3200001}}{2*50000}=\frac{-5+5\sqrt{3200001}}{100000} $
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