x((1)/(2)x-3)=476

Solution for x((1)/(2)x-3)=476 equation:

x((1)/(2)x-3)=476

We move all terms to the left:

x((1)/(2)x-3)-(476)=0


Domain of the equation: 2x-3)!=0

x∈R


We multiply parentheses

x^2-3x-476=0

a = 1; b = -3; c = -476;
Δ = b2-4ac
Δ = -32-4·1·(-476)
Δ = 1913
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{1913}}{2*1}=\frac{3-\sqrt{1913}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{1913}}{2*1}=\frac{3+\sqrt{1913}}{2}
$