x(x/2+1)=364

Solution for x(x/2+1)=364 equation:

x(x/2+1)=364

We move all terms to the left:

x(x/2+1)-(364)=0

We multiply parentheses

x^2+x-364=0

a = 1; b = 1; c = -364;
Δ = b2-4ac
Δ = 12-4·1·(-364)
Δ = 1457
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{-(1)-\sqrt{1457}}{2*1}=\frac{-1-\sqrt{1457}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1457}}{2*1}=\frac{-1+\sqrt{1457}}{2}
$