x=14x-2x^2

Solution for x=14x-2x^2 equation:

x=14x-2x^2

We move all terms to the left:

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

We get rid of parentheses

2x^2-14x+x=0

We add all the numbers together, and all the variables

2x^2-13x=0

a = 2; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·2·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*2}=\frac{26}{4}
=6+1/2
$