(X2-x-94)3/4-5=3

Solution for (X2-x-94)3/4-5=3 equation:

(X2-X-94)3/4-5=3

We move all terms to the left:

(X2-X-94)3/4-5-(3)=0

We add all the numbers together, and all the variables

(+X^2-1X-94)3/4-5-3=0

We add all the numbers together, and all the variables

(+X^2-1X-94)3/4-8=0

We multiply all the terms by the denominator


(+X^2-1X-94)3-8*4=0

We add all the numbers together, and all the variables

(+X^2-1X-94)3-32=0

We multiply parentheses

3X^2-3X-282-32=0

We add all the numbers together, and all the variables

3X^2-3X-314=0

a = 3; b = -3; c = -314;
Δ = b2-4ac
Δ = -32-4·3·(-314)
Δ = 3777
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{-(-3)-\sqrt{3777}}{2*3}=\frac{3-\sqrt{3777}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{3777}}{2*3}=\frac{3+\sqrt{3777}}{6}
$