5/2x+3=6x+3

Solution for 5/2x+3=6x+3 equation:

5/2x+3=6x+3

We move all terms to the left:

5/2x+3-(6x+3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

5/2x-6x-3+3=0

We multiply all the terms by the denominator


-6x*2x-3*2x+3*2x+5=0

Wy multiply elements

-12x^2-6x+6x+5=0

We add all the numbers together, and all the variables

-12x^2+5=0

a = -12; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-12)·5
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*-12}=\frac{0-4\sqrt{15}}{-24}
=-\frac{4\sqrt{15}}{-24}
=-\frac{\sqrt{15}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*-12}=\frac{0+4\sqrt{15}}{-24}
=\frac{4\sqrt{15}}{-24}
=\frac{\sqrt{15}}{-6}
$