5/2x+3=6x-2

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

5/2x+3=6x-2

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-12x^2+10x+5=0

a = -12; b = 10; c = +5;
Δ = b2-4ac
Δ = 102-4·(-12)·5
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{85}}{2*-12}=\frac{-10-2\sqrt{85}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{85}}{2*-12}=\frac{-10+2\sqrt{85}}{-24}
$