(1/2x-3)(x)=360

Solution for (1/2x-3)(x)=360 equation:

(1/2x-3)(x)=360

We move all terms to the left:

(1/2x-3)(x)-(360)=0


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

x∈R


We multiply parentheses

x^2-3x-360=0

a = 1; b = -3; c = -360;
Δ = b2-4ac
Δ = -32-4·1·(-360)
Δ = 1449
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:

$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{161}}{2*1}=\frac{3-3\sqrt{161}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{161}}{2*1}=\frac{3+3\sqrt{161}}{2}
$