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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-8x^2-40x+4x-1=0

We add all the numbers together, and all the variables

-8x^2-36x-1=0

a = -8; b = -36; c = -1;
Δ = b2-4ac
Δ = -362-4·(-8)·(-1)
Δ = 1264
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:

$\sqrt{\Delta}=\sqrt{1264}=\sqrt{16*79}=\sqrt{16}*\sqrt{79}=4\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{79}}{2*-8}=\frac{36-4\sqrt{79}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{79}}{2*-8}=\frac{36+4\sqrt{79}}{-16}
$