5/2x+3=4x+1/2x-2

Solution for 5/2x+3=4x+1/2x-2 equation:

5/2x+3=4x+1/2x-2

We move all terms to the left:

5/2x+3-(4x+1/2x-2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x-2)!=0

x∈R


We get rid of parentheses

5/2x-4x-1/2x+2+3=0

We multiply all the terms by the denominator


-4x*2x+2*2x+3*2x+5-1=0

We add all the numbers together, and all the variables

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

Wy multiply elements

-8x^2+4x+6x+4=0

We add all the numbers together, and all the variables

-8x^2+10x+4=0

a = -8; b = 10; c = +4;
Δ = b2-4ac
Δ = 102-4·(-8)·4
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{57}}{2*-8}=\frac{-10-2\sqrt{57}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{57}}{2*-8}=\frac{-10+2\sqrt{57}}{-16}
$