2/2x=7/5x+4

Solution for 2/2x=7/5x+4 equation:

2/2x=7/5x+4

We move all terms to the left:

2/2x-(7/5x+4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x+4)!=0

x∈R


We get rid of parentheses

2/2x-7/5x-4=0

We calculate fractions


10x/10x^2+(-14x)/10x^2-4=0

We multiply all the terms by the denominator


10x+(-14x)-4*10x^2=0

Wy multiply elements

-40x^2+10x+(-14x)=0

We get rid of parentheses

-40x^2+10x-14x=0

We add all the numbers together, and all the variables

-40x^2-4x=0

a = -40; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-40)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-40}=\frac{0}{-80}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-40}=\frac{8}{-80}
=-1/10
$