1/2x-2x+5=-20

Solution for 1/2x-2x+5=-20 equation:

1/2x-2x+5=-20

We move all terms to the left:

1/2x-2x+5-(-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

-2x+1/2x+25=0

We multiply all the terms by the denominator


-2x*2x+25*2x+1=0

Wy multiply elements

-4x^2+50x+1=0

a = -4; b = 50; c = +1;
Δ = b2-4ac
Δ = 502-4·(-4)·1
Δ = 2516
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:

$\sqrt{\Delta}=\sqrt{2516}=\sqrt{4*629}=\sqrt{4}*\sqrt{629}=2\sqrt{629}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{629}}{2*-4}=\frac{-50-2\sqrt{629}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{629}}{2*-4}=\frac{-50+2\sqrt{629}}{-8}
$