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+30x+4=0

a = -10; b = 30; c = +4;
Δ = b2-4ac
Δ = 302-4·(-10)·4
Δ = 1060
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:

$\sqrt{\Delta}=\sqrt{1060}=\sqrt{4*265}=\sqrt{4}*\sqrt{265}=2\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{265}}{2*-10}=\frac{-30-2\sqrt{265}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{265}}{2*-10}=\frac{-30+2\sqrt{265}}{-20}
$