(1/2x-9)x=180

Solution for (1/2x-9)x=180 equation:

(1/2x-9)x=180

We move all terms to the left:

(1/2x-9)x-(180)=0


Domain of the equation: 2x-9)x!=0

x∈R


We multiply parentheses

x^2-9x-180=0

a = 1; b = -9; c = -180;
Δ = b2-4ac
Δ = -92-4·1·(-180)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{89}}{2*1}=\frac{9-3\sqrt{89}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{89}}{2*1}=\frac{9+3\sqrt{89}}{2}
$