5/4x+3-3x=7/4x-14

Solution for 5/4x+3-3x=7/4x-14 equation:

5/4x+3-3x=7/4x-14

We move all terms to the left:

5/4x+3-3x-(7/4x-14)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 4x-14)!=0

x∈R


We add all the numbers together, and all the variables

-3x+5/4x-(7/4x-14)+3=0

We get rid of parentheses

-3x+5/4x-7/4x+14+3=0

We multiply all the terms by the denominator


-3x*4x+14*4x+3*4x+5-7=0

We add all the numbers together, and all the variables

-3x*4x+14*4x+3*4x-2=0

Wy multiply elements

-12x^2+56x+12x-2=0

We add all the numbers together, and all the variables

-12x^2+68x-2=0

a = -12; b = 68; c = -2;
Δ = b2-4ac
Δ = 682-4·(-12)·(-2)
Δ = 4528
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4528}=\sqrt{16*283}=\sqrt{16}*\sqrt{283}=4\sqrt{283}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-4\sqrt{283}}{2*-12}=\frac{-68-4\sqrt{283}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+4\sqrt{283}}{2*-12}=\frac{-68+4\sqrt{283}}{-24}
$