x(x-6)=374

Solution for x(x-6)=374 equation:

x(x-6)=374

We move all terms to the left:

x(x-6)-(374)=0

We multiply parentheses

x^2-6x-374=0

a = 1; b = -6; c = -374;
Δ = b2-4ac
Δ = -62-4·1·(-374)
Δ = 1532
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:

$\sqrt{\Delta}=\sqrt{1532}=\sqrt{4*383}=\sqrt{4}*\sqrt{383}=2\sqrt{383}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{383}}{2*1}=\frac{6-2\sqrt{383}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{383}}{2*1}=\frac{6+2\sqrt{383}}{2}
$