X^2-8x+14=2x

Solution for X^2-8x+14=2x equation:

X^2-8X+14=2X

We move all terms to the left:

X^2-8X+14-(2X)=0

We add all the numbers together, and all the variables

X^2-10X+14=0

a = 1; b = -10; c = +14;
Δ = b2-4ac
Δ = -102-4·1·14
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{11}}{2*1}=\frac{10-2\sqrt{11}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{11}}{2*1}=\frac{10+2\sqrt{11}}{2}
$