x^2-x+14=2x(x-3)

Solution for x^2-x+14=2x(x-3) equation:

x^2-x+14=2x(x-3)

We move all terms to the left:

x^2-x+14-(2x(x-3))=0

We add all the numbers together, and all the variables

x^2-1x-(2x(x-3))+14=0


We calculate terms in parentheses: -(2x(x-3)), so:

2x(x-3)

We multiply parentheses

2x^2-6x

Back to the equation:

-(2x^2-6x)


We get rid of parentheses

x^2-2x^2-1x+6x+14=0

We add all the numbers together, and all the variables

-1x^2+5x+14=0

a = -1; b = 5; c = +14;
Δ = b2-4ac
Δ = 52-4·(-1)·14
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-9}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+9}{2*-1}=\frac{4}{-2}
=-2
$