14/2x-12/3=7x-4

Solution for 14/2x-12/3=7x-4 equation:

14/2x-12/3=7x-4

We move all terms to the left:

14/2x-12/3-(7x-4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

14/2x-(7x-4)-4=0

We get rid of parentheses

14/2x-7x+4-4=0

We multiply all the terms by the denominator


-7x*2x+4*2x-4*2x+14=0

Wy multiply elements

-14x^2+8x-8x+14=0

We add all the numbers together, and all the variables

-14x^2+14=0

a = -14; b = 0; c = +14;
Δ = b2-4ac
Δ = 02-4·(-14)·14
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{-(0)-28}{2*-14}=\frac{-28}{-28}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28}{2*-14}=\frac{28}{-28}
=-1
$