-x+5=5(x-5)x=

Solution for -x+5=5(x-5)x= equation:

-x+5=5(x-5)x=

We move all terms to the left:

-x+5-(5(x-5)x)=0

We add all the numbers together, and all the variables

-1x-(5(x-5)x)+5=0


We calculate terms in parentheses: -(5(x-5)x), so:

5(x-5)x

We multiply parentheses

5x^2-25x

Back to the equation:

-(5x^2-25x)


We get rid of parentheses

-5x^2-1x+25x+5=0

We add all the numbers together, and all the variables

-5x^2+24x+5=0

a = -5; b = 24; c = +5;
Δ = b2-4ac
Δ = 242-4·(-5)·5
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-26}{2*-5}=\frac{-50}{-10}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+26}{2*-5}=\frac{2}{-10}
=-1/5
$