5*(5x-10)=25x*(x-2)

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Solution for 5*(5x-10)=25x*(x-2) equation:



5(5x-10)=25x(x-2)
We move all terms to the left:
5(5x-10)-(25x(x-2))=0
We multiply parentheses
25x-(25x(x-2))-50=0
We calculate terms in parentheses: -(25x(x-2)), so:
25x(x-2)
We multiply parentheses
25x^2-50x
Back to the equation:
-(25x^2-50x)
We get rid of parentheses
-25x^2+25x+50x-50=0
We add all the numbers together, and all the variables
-25x^2+75x-50=0
a = -25; b = 75; c = -50;
Δ = b2-4ac
Δ = 752-4·(-25)·(-50)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-25}{2*-25}=\frac{-100}{-50} =+2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+25}{2*-25}=\frac{-50}{-50} =1 $

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