7/2x-5=4/6x+12

Solution for 7/2x-5=4/6x+12 equation:

7/2x-5=4/6x+12

We move all terms to the left:

7/2x-5-(4/6x+12)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x+12)!=0

x∈R


We get rid of parentheses

7/2x-4/6x-12-5=0

We calculate fractions


42x/12x^2+(-8x)/12x^2-12-5=0

We add all the numbers together, and all the variables

42x/12x^2+(-8x)/12x^2-17=0

We multiply all the terms by the denominator


42x+(-8x)-17*12x^2=0

Wy multiply elements

-204x^2+42x+(-8x)=0

We get rid of parentheses

-204x^2+42x-8x=0

We add all the numbers together, and all the variables

-204x^2+34x=0

a = -204; b = 34; c = 0;
Δ = b2-4ac
Δ = 342-4·(-204)·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-34}{2*-204}=\frac{-68}{-408}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+34}{2*-204}=\frac{0}{-408}
=0
$