1/2x-9x+20=0

Solution for 1/2x-9x+20=0 equation:

1/2x-9x+20=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-9x+1/2x+20=0

We multiply all the terms by the denominator


-9x*2x+20*2x+1=0

Wy multiply elements

-18x^2+40x+1=0

a = -18; b = 40; c = +1;
Δ = b2-4ac
Δ = 402-4·(-18)·1
Δ = 1672
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:

$\sqrt{\Delta}=\sqrt{1672}=\sqrt{4*418}=\sqrt{4}*\sqrt{418}=2\sqrt{418}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{418}}{2*-18}=\frac{-40-2\sqrt{418}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{418}}{2*-18}=\frac{-40+2\sqrt{418}}{-36}
$