4/5x+2=2x+4

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

4/5x+2=2x+4

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-10x^2-20x+10x+4=0

We add all the numbers together, and all the variables

-10x^2-10x+4=0

a = -10; b = -10; c = +4;
Δ = b2-4ac
Δ = -102-4·(-10)·4
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{65}}{2*-10}=\frac{10-2\sqrt{65}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{65}}{2*-10}=\frac{10+2\sqrt{65}}{-20}
$