16x-5=7/3x+4

Solution for 16x-5=7/3x+4 equation:

16x-5=7/3x+4

We move all terms to the left:

16x-5-(7/3x+4)=0


Domain of the equation: 3x+4)!=0

x∈R


We get rid of parentheses

16x-7/3x-4-5=0

We multiply all the terms by the denominator


16x*3x-4*3x-5*3x-7=0

Wy multiply elements

48x^2-12x-15x-7=0

We add all the numbers together, and all the variables

48x^2-27x-7=0

a = 48; b = -27; c = -7;
Δ = b2-4ac
Δ = -272-4·48·(-7)
Δ = 2073
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-\sqrt{2073}}{2*48}=\frac{27-\sqrt{2073}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{2073}}{2*48}=\frac{27+\sqrt{2073}}{96}
$