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

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
$