5/2x+5=3x-1

Solution for 5/2x+5=3x-1 equation:

5/2x+5=3x-1

We move all terms to the left:

5/2x+5-(3x-1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

5/2x-3x+1+5=0

We multiply all the terms by the denominator


-3x*2x+1*2x+5*2x+5=0

Wy multiply elements

-6x^2+2x+10x+5=0

We add all the numbers together, and all the variables

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

a = -6; b = 12; c = +5;
Δ = b2-4ac
Δ = 122-4·(-6)·5
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{66}}{2*-6}=\frac{-12-2\sqrt{66}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{66}}{2*-6}=\frac{-12+2\sqrt{66}}{-12}
$