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

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

8-1/2X=6-1/5X

We move all terms to the left:

8-1/2X-(6-1/5X)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R



Domain of the equation: 5X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-1/2X+1/5X-6+8=0

We calculate fractions


(-5X)/10X^2+2X/10X^2-6+8=0

We add all the numbers together, and all the variables

(-5X)/10X^2+2X/10X^2+2=0

We multiply all the terms by the denominator


(-5X)+2X+2*10X^2=0

We add all the numbers together, and all the variables

2X+(-5X)+2*10X^2=0

Wy multiply elements

20X^2+2X+(-5X)=0

We get rid of parentheses

20X^2+2X-5X=0

We add all the numbers together, and all the variables

20X^2-3X=0

a = 20; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·20·0
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*20}=\frac{0}{40}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*20}=\frac{6}{40}
=3/20
$