8/5x-2=1/2x+6

Solution for 8/5x-2=1/2x+6 equation:

8/5x-2=1/2x+6

We move all terms to the left:

8/5x-2-(1/2x+6)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x+6)!=0

x∈R


We get rid of parentheses

8/5x-1/2x-6-2=0

We calculate fractions


16x/10x^2+(-5x)/10x^2-6-2=0

We add all the numbers together, and all the variables

16x/10x^2+(-5x)/10x^2-8=0

We multiply all the terms by the denominator


16x+(-5x)-8*10x^2=0

Wy multiply elements

-80x^2+16x+(-5x)=0

We get rid of parentheses

-80x^2+16x-5x=0

We add all the numbers together, and all the variables

-80x^2+11x=0

a = -80; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-80)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-80}=\frac{-22}{-160}
=11/80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-80}=\frac{0}{-160}
=0
$