5/2x+3=6x+4

Solution for 5/2x+3=6x+4 equation:

5/2x+3=6x+4

We move all terms to the left:

5/2x+3-(6x+4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

5/2x-6x-4+3=0

We multiply all the terms by the denominator


-6x*2x-4*2x+3*2x+5=0

Wy multiply elements

-12x^2-8x+6x+5=0

We add all the numbers together, and all the variables

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

a = -12; b = -2; c = +5;
Δ = b2-4ac
Δ = -22-4·(-12)·5
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{61}}{2*-12}=\frac{2-2\sqrt{61}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{61}}{2*-12}=\frac{2+2\sqrt{61}}{-24}
$