6/2x+8=1/5x+9

Solution for 6/2x+8=1/5x+9 equation:

6/2x+8=1/5x+9

We move all terms to the left:

6/2x+8-(1/5x+9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x+9)!=0

x∈R


We get rid of parentheses

6/2x-1/5x-9+8=0

We calculate fractions


30x/10x^2+(-2x)/10x^2-9+8=0

We add all the numbers together, and all the variables

30x/10x^2+(-2x)/10x^2-1=0

We multiply all the terms by the denominator


30x+(-2x)-1*10x^2=0

Wy multiply elements

-10x^2+30x+(-2x)=0

We get rid of parentheses

-10x^2+30x-2x=0

We add all the numbers together, and all the variables

-10x^2+28x=0

a = -10; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-10)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-10}=\frac{-56}{-20}
=2+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-10}=\frac{0}{-20}
=0
$