.5(2x-9)x=50

Solution for .5(2x-9)x=50 equation:

.5(2x-9)x=50

We move all terms to the left:

.5(2x-9)x-(50)=0

We multiply parentheses

0x^2+0x-50=0

We add all the numbers together, and all the variables

x^2+x-50=0

a = 1; b = 1; c = -50;
Δ = b2-4ac
Δ = 12-4·1·(-50)
Δ = 201
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{201}}{2*1}=\frac{-1-\sqrt{201}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{201}}{2*1}=\frac{-1+\sqrt{201}}{2}
$