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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-1/2x-(4x-2)-19=0

We get rid of parentheses

-1/2x-4x+2-19=0

We multiply all the terms by the denominator


-4x*2x+2*2x-19*2x-1=0

Wy multiply elements

-8x^2+4x-38x-1=0

We add all the numbers together, and all the variables

-8x^2-34x-1=0

a = -8; b = -34; c = -1;
Δ = b2-4ac
Δ = -342-4·(-8)·(-1)
Δ = 1124
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:

$\sqrt{\Delta}=\sqrt{1124}=\sqrt{4*281}=\sqrt{4}*\sqrt{281}=2\sqrt{281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{281}}{2*-8}=\frac{34-2\sqrt{281}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{281}}{2*-8}=\frac{34+2\sqrt{281}}{-16}
$