3x*23/x=16x+3

Solution for 3x*23/x=16x+3 equation:

3x*23/x=16x+3

We move all terms to the left:

3x*23/x-(16x+3)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

3x*23/x-16x-3=0

We multiply all the terms by the denominator


3x*23-16x*x-3*x=0

We add all the numbers together, and all the variables

-3x+3x*23-16x*x=0

Wy multiply elements

-16x^2-3x+69x=0

We add all the numbers together, and all the variables

-16x^2+66x=0

a = -16; b = 66; c = 0;
Δ = b2-4ac
Δ = 662-4·(-16)·0
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-66}{2*-16}=\frac{-132}{-32}
=4+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+66}{2*-16}=\frac{0}{-32}
=0
$