(x+10)=2x(x+10)

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

(x+10)=2x(x+10)

We move all terms to the left:

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

We get rid of parentheses

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


We calculate terms in parentheses: -(2x(x+10)), so:

2x(x+10)

We multiply parentheses

2x^2+20x

Back to the equation:

-(2x^2+20x)


We get rid of parentheses

-2x^2+x-20x+10=0

We add all the numbers together, and all the variables

-2x^2-19x+10=0

a = -2; b = -19; c = +10;
Δ = b2-4ac
Δ = -192-4·(-2)·10
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-21}{2*-2}=\frac{-2}{-4}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+21}{2*-2}=\frac{40}{-4}
=-10
$