32/3x+5=5x

Solution for 32/3x+5=5x equation:

32/3x+5=5x

We move all terms to the left:

32/3x+5-(5x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-5x+32/3x+5=0

We multiply all the terms by the denominator


-5x*3x+5*3x+32=0

Wy multiply elements

-15x^2+15x+32=0

a = -15; b = 15; c = +32;
Δ = b2-4ac
Δ = 152-4·(-15)·32
Δ = 2145
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{-(15)-\sqrt{2145}}{2*-15}=\frac{-15-\sqrt{2145}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{2145}}{2*-15}=\frac{-15+\sqrt{2145}}{-30}
$