x+1=56/2x+3

Solution for x+1=56/2x+3 equation:

x+1=56/2x+3

We move all terms to the left:

x+1-(56/2x+3)=0


Domain of the equation: 2x+3)!=0

x∈R


We get rid of parentheses

x-56/2x-3+1=0

We multiply all the terms by the denominator


x*2x-3*2x+1*2x-56=0

Wy multiply elements

2x^2-6x+2x-56=0

We add all the numbers together, and all the variables

2x^2-4x-56=0

a = 2; b = -4; c = -56;
Δ = b2-4ac
Δ = -42-4·2·(-56)
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{29}}{2*2}=\frac{4-4\sqrt{29}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{29}}{2*2}=\frac{4+4\sqrt{29}}{4}
$