X+3=5/2x+1

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

X+3=5/2X+1

We move all terms to the left:

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


Domain of the equation: 2X+1)!=0

X∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

2X^2-2X+6X-5=0

We add all the numbers together, and all the variables

2X^2+4X-5=0

a = 2; b = 4; c = -5;
Δ = b2-4ac
Δ = 42-4·2·(-5)
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{14}}{2*2}=\frac{-4-2\sqrt{14}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{14}}{2*2}=\frac{-4+2\sqrt{14}}{4}
$