1/2x+2=4/5x+5

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

1/2x+2=4/5x+5

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


5x/10x^2+(-8x)/10x^2-5+2=0

We add all the numbers together, and all the variables

5x/10x^2+(-8x)/10x^2-3=0

We multiply all the terms by the denominator


5x+(-8x)-3*10x^2=0

Wy multiply elements

-30x^2+5x+(-8x)=0

We get rid of parentheses

-30x^2+5x-8x=0

We add all the numbers together, and all the variables

-30x^2-3x=0

a = -30; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-30)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-30}=\frac{0}{-60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-30}=\frac{6}{-60}
=-1/10
$