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

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

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

We move all terms to the left:

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

We use the square of the difference formula

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


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

(+5x)

We get rid of parentheses

5x

Back to the equation:

-(5x)


a = 1; b = -5; c = -25;
Δ = b2-4ac
Δ = -52-4·1·(-25)
Δ = 125
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:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{5}}{2*1}=\frac{5-5\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{5}}{2*1}=\frac{5+5\sqrt{5}}{2}
$