(x+5)2=5x(x-1)

Solution for (x+5)2=5x(x-1) equation:

(x+5)2=5x(x-1)

We move all terms to the left:

(x+5)2-(5x(x-1))=0

We multiply parentheses

2x-(5x(x-1))+10=0


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

5x(x-1)

We multiply parentheses

5x^2-5x

Back to the equation:

-(5x^2-5x)


We get rid of parentheses

-5x^2+2x+5x+10=0

We add all the numbers together, and all the variables

-5x^2+7x+10=0

a = -5; b = 7; c = +10;
Δ = b2-4ac
Δ = 72-4·(-5)·10
Δ = 249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{249}}{2*-5}=\frac{-7-\sqrt{249}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{249}}{2*-5}=\frac{-7+\sqrt{249}}{-10}
$