X=x^2-3x/416

Solution for X=x^2-3x/416 equation:

X=X^2-3X/416

We move all terms to the left:

X-(X^2-3X/416)=0

We get rid of parentheses

-X^2+X+3X/416=0

We multiply all the terms by the denominator


-X^2*416+X*416+3X=0

We add all the numbers together, and all the variables

-X^2*416+3X+X*416=0

Wy multiply elements

-416X^2+3X+416X=0

We add all the numbers together, and all the variables

-416X^2+419X=0

a = -416; b = 419; c = 0;
Δ = b2-4ac
Δ = 4192-4·(-416)·0
Δ = 175561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{175561}=419$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(419)-419}{2*-416}=\frac{-838}{-832}
=1+3/416
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(419)+419}{2*-416}=\frac{0}{-832}
=0
$