5x(5x+1)=125

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Solution for 5x(5x+1)=125 equation:



5x(5x+1)=125
We move all terms to the left:
5x(5x+1)-(125)=0
We multiply parentheses
25x^2+5x-125=0
a = 25; b = 5; c = -125;
Δ = b2-4ac
Δ = 52-4·25·(-125)
Δ = 12525
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:
$\sqrt{\Delta}=\sqrt{12525}=\sqrt{25*501}=\sqrt{25}*\sqrt{501}=5\sqrt{501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{501}}{2*25}=\frac{-5-5\sqrt{501}}{50} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{501}}{2*25}=\frac{-5+5\sqrt{501}}{50} $

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