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+7=0

We multiply all the terms by the denominator


5x+(-8x)+7*10x^2=0

Wy multiply elements

70x^2+5x+(-8x)=0

We get rid of parentheses

70x^2+5x-8x=0

We add all the numbers together, and all the variables

70x^2-3x=0

a = 70; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·70·0
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*70}=\frac{0}{140}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*70}=\frac{6}{140}
=3/70
$