12-21x2+5x2=x

Solution for 12-21x2+5x2=x equation:

12-21x^2+5x^2=x

We move all terms to the left:

12-21x^2+5x^2-(x)=0

We add all the numbers together, and all the variables

-16x^2-1x+12=0

a = -16; b = -1; c = +12;
Δ = b2-4ac
Δ = -12-4·(-16)·12
Δ = 769
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{769}}{2*-16}=\frac{1-\sqrt{769}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{769}}{2*-16}=\frac{1+\sqrt{769}}{-32}
$