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5x^2-4x=1/125
We move all terms to the left:
5x^2-4x-(1/125)=0
We add all the numbers together, and all the variables
5x^2-4x-(+1/125)=0
We get rid of parentheses
5x^2-4x-1/125=0
We multiply all the terms by the denominator
5x^2*125-4x*125-1=0
Wy multiply elements
625x^2-500x-1=0
a = 625; b = -500; c = -1;
Δ = b2-4ac
Δ = -5002-4·625·(-1)
Δ = 252500
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{252500}=\sqrt{2500*101}=\sqrt{2500}*\sqrt{101}=50\sqrt{101}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-50\sqrt{101}}{2*625}=\frac{500-50\sqrt{101}}{1250} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+50\sqrt{101}}{2*625}=\frac{500+50\sqrt{101}}{1250} $
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