(X-2)(x)(x)=3174

Solution for (X-2)(x)(x)=3174 equation:

(X-2)(X)(X)=3174

We move all terms to the left:

(X-2)(X)(X)-(3174)=0

We multiply parentheses

X^2-2X-3174=0

a = 1; b = -2; c = -3174;
Δ = b2-4ac
Δ = -22-4·1·(-3174)
Δ = 12700
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12700}=\sqrt{100*127}=\sqrt{100}*\sqrt{127}=10\sqrt{127}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10\sqrt{127}}{2*1}=\frac{2-10\sqrt{127}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10\sqrt{127}}{2*1}=\frac{2+10\sqrt{127}}{2}
$