X2-2x+12=2x(x+10)

Solution for X2-2x+12=2x(x+10) equation:

X2-2X+12=2X(X+10)

We move all terms to the left:

X2-2X+12-(2X(X+10))=0

We add all the numbers together, and all the variables

X^2-2X-(2X(X+10))+12=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

X^2-2X^2-2X-20X+12=0

We add all the numbers together, and all the variables

-1X^2-22X+12=0

a = -1; b = -22; c = +12;
Δ = b2-4ac
Δ = -222-4·(-1)·12
Δ = 532
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:

$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{133}}{2*-1}=\frac{22-2\sqrt{133}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{133}}{2*-1}=\frac{22+2\sqrt{133}}{-2}
$