7-3/2x=12+-5/3x

Solution for 7-3/2x=12+-5/3x equation:

7-3/2x=12+-5/3x

We move all terms to the left:

7-3/2x-(12+-5/3x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-3/2x-(-5/3x)+7=0

We get rid of parentheses

-3/2x+5/3x+7=0

We calculate fractions


(-9x)/6x^2+10x/6x^2+7=0

We multiply all the terms by the denominator


(-9x)+10x+7*6x^2=0

We add all the numbers together, and all the variables

10x+(-9x)+7*6x^2=0

Wy multiply elements

42x^2+10x+(-9x)=0

We get rid of parentheses

42x^2+10x-9x=0

We add all the numbers together, and all the variables

42x^2+x=0

a = 42; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·42·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*42}=\frac{-2}{84}
=-1/42
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*42}=\frac{0}{84}
=0
$