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x*10^x=500000
We move all terms to the left:
x*10^x-(500000)=0
Wy multiply elements
10x^2-500000=0
a = 10; b = 0; c = -500000;
Δ = b2-4ac
Δ = 02-4·10·(-500000)
Δ = 20000000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20000000}=\sqrt{4000000*5}=\sqrt{4000000}*\sqrt{5}=2000\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2000\sqrt{5}}{2*10}=\frac{0-2000\sqrt{5}}{20} =-\frac{2000\sqrt{5}}{20} =-100\sqrt{5} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2000\sqrt{5}}{2*10}=\frac{0+2000\sqrt{5}}{20} =\frac{2000\sqrt{5}}{20} =100\sqrt{5} $
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