2/4x+2=5x-43

Solution for 2/4x+2=5x-43 equation:

2/4x+2=5x-43

We move all terms to the left:

2/4x+2-(5x-43)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

2/4x-5x+43+2=0

We multiply all the terms by the denominator


-5x*4x+43*4x+2*4x+2=0

Wy multiply elements

-20x^2+172x+8x+2=0

We add all the numbers together, and all the variables

-20x^2+180x+2=0

a = -20; b = 180; c = +2;
Δ = b2-4ac
Δ = 1802-4·(-20)·2
Δ = 32560
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:

$\sqrt{\Delta}=\sqrt{32560}=\sqrt{16*2035}=\sqrt{16}*\sqrt{2035}=4\sqrt{2035}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-4\sqrt{2035}}{2*-20}=\frac{-180-4\sqrt{2035}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+4\sqrt{2035}}{2*-20}=\frac{-180+4\sqrt{2035}}{-40}
$