X/3x+14=5x-4

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

X/3X+14=5X-4

We move all terms to the left:

X/3X+14-(5X-4)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We get rid of parentheses

X/3X-5X+4+14=0

We multiply all the terms by the denominator


X-5X*3X+4*3X+14*3X=0

Wy multiply elements

-15X^2+X+12X+42X=0

We add all the numbers together, and all the variables

-15X^2+55X=0

a = -15; b = 55; c = 0;
Δ = b2-4ac
Δ = 552-4·(-15)·0
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-55}{2*-15}=\frac{-110}{-30}
=3+2/3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+55}{2*-15}=\frac{0}{-30}
=0
$