1/2x+20=5x-4

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

1/2x+20=5x-4

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-10x^2+48x+1=0

a = -10; b = 48; c = +1;
Δ = b2-4ac
Δ = 482-4·(-10)·1
Δ = 2344
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:

$\sqrt{\Delta}=\sqrt{2344}=\sqrt{4*586}=\sqrt{4}*\sqrt{586}=2\sqrt{586}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-2\sqrt{586}}{2*-10}=\frac{-48-2\sqrt{586}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+2\sqrt{586}}{2*-10}=\frac{-48+2\sqrt{586}}{-20}
$