(x+5)(x-5)=x(-5x-10)

Solution for (x+5)(x-5)=x(-5x-10) equation:

(x+5)(x-5)=x(-5x-10)

We move all terms to the left:

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

We use the square of the difference formula

x^2-(x(-5x-10))-25=0


We calculate terms in parentheses: -(x(-5x-10)), so:

x(-5x-10)

We multiply parentheses

-5x^2-10x

Back to the equation:

-(-5x^2-10x)


We get rid of parentheses

x^2+5x^2+10x-25=0

We add all the numbers together, and all the variables

6x^2+10x-25=0

a = 6; b = 10; c = -25;
Δ = b2-4ac
Δ = 102-4·6·(-25)
Δ = 700
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{7}}{2*6}=\frac{-10-10\sqrt{7}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{7}}{2*6}=\frac{-10+10\sqrt{7}}{12}
$