-1/2x-20=4x-5

Solution for -1/2x-20=4x-5 equation:

-1/2x-20=4x-5

We move all terms to the left:

-1/2x-20-(4x-5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

-1/2x-4x+5-20=0

We multiply all the terms by the denominator


-4x*2x+5*2x-20*2x-1=0

Wy multiply elements

-8x^2+10x-40x-1=0

We add all the numbers together, and all the variables

-8x^2-30x-1=0

a = -8; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·(-8)·(-1)
Δ = 868
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:

$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{217}}{2*-8}=\frac{30-2\sqrt{217}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{217}}{2*-8}=\frac{30+2\sqrt{217}}{-16}
$