X2-5x=5(5-x)

Solution for X2-5x=5(5-x) equation:

X2-5X=5(5-X)

We move all terms to the left:

X2-5X-(5(5-X))=0

We add all the numbers together, and all the variables

X2-5X-(5(-1X+5))=0

We add all the numbers together, and all the variables

X^2-5X-(5(-1X+5))=0


We calculate terms in parentheses: -(5(-1X+5)), so:

5(-1X+5)

We multiply parentheses

-5X+25

Back to the equation:

-(-5X+25)


We get rid of parentheses

X^2-5X+5X-25=0

We add all the numbers together, and all the variables

X^2-25=0

a = 1; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·1·(-25)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10}{2*1}=\frac{-10}{2}
=-5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10}{2*1}=\frac{10}{2}
=5
$