2x-10=x(x+10)

Solution for 2x-10=x(x+10) equation:

2x-10=x(x+10)

We move all terms to the left:

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


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

x(x+10)

We multiply parentheses

x^2+10x

Back to the equation:

-(x^2+10x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2-8x-10=0

a = -1; b = -8; c = -10;
Δ = b2-4ac
Δ = -82-4·(-1)·(-10)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{6}}{2*-1}=\frac{8-2\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{6}}{2*-1}=\frac{8+2\sqrt{6}}{-2}
$