-3/2x+15=-2/6x+8

Solution for -3/2x+15=-2/6x+8 equation:

-3/2x+15=-2/6x+8

We move all terms to the left:

-3/2x+15-(-2/6x+8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x+8)!=0

x∈R


We get rid of parentheses

-3/2x+2/6x-8+15=0

We calculate fractions


(-18x)/12x^2+4x/12x^2-8+15=0

We add all the numbers together, and all the variables

(-18x)/12x^2+4x/12x^2+7=0

We multiply all the terms by the denominator


(-18x)+4x+7*12x^2=0

We add all the numbers together, and all the variables

4x+(-18x)+7*12x^2=0

Wy multiply elements

84x^2+4x+(-18x)=0

We get rid of parentheses

84x^2+4x-18x=0

We add all the numbers together, and all the variables

84x^2-14x=0

a = 84; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·84·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*84}=\frac{0}{168}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*84}=\frac{28}{168}
=1/6
$