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x+5/100x=252
We move all terms to the left:
x+5/100x-(252)=0
Domain of the equation: 100x!=0We multiply all the terms by the denominator
x!=0/100
x!=0
x∈R
x*100x-252*100x+5=0
Wy multiply elements
100x^2-25200x+5=0
a = 100; b = -25200; c = +5;
Δ = b2-4ac
Δ = -252002-4·100·5
Δ = 635038000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{635038000}=\sqrt{400*1587595}=\sqrt{400}*\sqrt{1587595}=20\sqrt{1587595}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25200)-20\sqrt{1587595}}{2*100}=\frac{25200-20\sqrt{1587595}}{200} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25200)+20\sqrt{1587595}}{2*100}=\frac{25200+20\sqrt{1587595}}{200} $
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