5/2x+6=2x-3

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

5/2x+6=2x-3

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2+6x+12x+5=0

We add all the numbers together, and all the variables

-4x^2+18x+5=0

a = -4; b = 18; c = +5;
Δ = b2-4ac
Δ = 182-4·(-4)·5
Δ = 404
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:

$\sqrt{\Delta}=\sqrt{404}=\sqrt{4*101}=\sqrt{4}*\sqrt{101}=2\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{101}}{2*-4}=\frac{-18-2\sqrt{101}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{101}}{2*-4}=\frac{-18+2\sqrt{101}}{-8}
$