x*(x-3)=194

Solution for x*(x-3)=194 equation:

x(x-3)=194

We move all terms to the left:

x(x-3)-(194)=0

We multiply parentheses

x^2-3x-194=0

a = 1; b = -3; c = -194;
Δ = b2-4ac
Δ = -32-4·1·(-194)
Δ = 785
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{785}}{2*1}=\frac{3-\sqrt{785}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{785}}{2*1}=\frac{3+\sqrt{785}}{2}
$