(X-1/2)^3-x(x+1/4)^2+23/16=0

Solution for (X-1/2)^3-x(x+1/4)^2+23/16=0 equation:

(X-1/2)^3-X(X+1/4)^2+23/16=0

We add all the numbers together, and all the variables

(+X-1/2)^3-X(+X+1/4)^2+23/16=0

We calculate fractions


((X-4)^2*16)/()+(-X(X+2)^3*16)/()+()/()=0


We calculate terms in parentheses: +((X-4)^2*16)/(), so:

(X-4)^2*16)/(

We multiply all the terms by the denominator


(X-4)^2*16)

We get rid of parentheses

X-4)^2*16

We add all the numbers together, and all the variables

X

Back to the equation:

+(X)



We calculate terms in parentheses: +(-X(X+2)^3*16)/(), so:

-X(X+2)^3*16)/(

We multiply all the terms by the denominator


-X(X+2)^3*16)

We multiply parentheses

-X^2-32X^2

We add all the numbers together, and all the variables

-33X^2

Back to the equation:

+(-33X^2)


We add all the numbers together, and all the variables

(-33X^2)+X+1=0

We get rid of parentheses

-33X^2+X+1=0

a = -33; b = 1; c = +1;
Δ = b2-4ac
Δ = 12-4·(-33)·1
Δ = 133
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{133}}{2*-33}=\frac{-1-\sqrt{133}}{-66}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{133}}{2*-33}=\frac{-1+\sqrt{133}}{-66}
$